My 2019 Mathematics A To Z: Buffon’s Needle

Today’s A To Z term was suggested by Peter Mander. Mander authors CarnotCycle, which when I first joined WordPress was one of the few blogs discussing thermodynamics in any detail. When I last checked it still was, which is a shame. Thermodynamics is a fascinating field. It’s as deeply weird and counter-intuitive and important as quantum mechanics. Yet its principles are as familiar as a mug of warm tea on a chilly day. Mander writes at a more technical level than I usually do. But if you’re comfortable with calculus, or if you’re comfortable nodding at a line and agreeing that he wouldn’t fib to you about a thing like calculus, it’s worth reading.

Art by Thomas K Dye, creator of the web comics Projection Edge, Newshounds, Infinity Refugees, and Something Happens. He’s on Twitter as @projectionedge. You can get to read Projection Edge six months early by subscribing to his Patreon.

Buffon’s Needle.

I’ve written of my fondness for boredom. A bored mind is not one lacking stimulation. It is one stimulated by anything, however petty. And in petty things we can find great surprises.

I do not know what caused Georges-Louis Leclerc, Comte de Buffon, to discover the needle problem named for him. It seems like something born of a bored but active mind. Buffon had an active mind: he was one of Europe’s most important naturalists of the 1700s. He also worked in mathematics, and astronomy, and optics. It shows what one can do with an engaged mind and a large inheritance from one’s childless uncle who’s the tax farmer for all Sicily.

The problem, though. Imagine dropping a needle on a floor that has equally spaced parallel lines. What is the probability that the needle will land on any of the lines? It could occur to anyone with a wood floor who’s dropped a thing. (There is a similar problem which would occur to anyone with a tile floor.) They have only to be ready to ask the question. Buffon did this in 1733. He had it solved by 1777. We, with several centuries’ insight into probability and calculus, need less than 44 years to solve the question.

Let me use L as the length of the needle. And d as the spacing of the parallel lines. If the needle’s length is less than the spacing then this is an easy formula to write, and not too hard to calculate. The probability, P, of the needle crossing some line is:

I won’t derive it rigorously. You don’t need me for that. The interesting question is whether this formula makes sense. That L and d are in it? Yes, that makes sense. The length of the needle and the gap between lines have to be in there. More, the probability has to have the ratio between the two. There’s different ways to argue this. Dimensional analysis convinces me, at least. Probability is a pure number. L is a measurement of length; d is a measurement of length. To get a pure number starting with L and d means one of them has to divide into the other. That L is in the numerator and d the denominator makes sense. A tiny needle has a tiny chance of crossing a line. A large needle has a large chance. That is raised to the first power, rather than the second or third or such … well, that’s fair. A needle twice as long having twice the chance of crossing a line? That sounds more likely than a needle twice as long having four times the chance, or eight times the chance.

Does the 2 belong there? Hard to say. 2 seems like a harmless enough number. It appears in many respectable formulas. That π, though …

That π …

π comes to us from circles. We see it in calculations about circles and spheres all the time. We’re doing a problem with lines and line segments. What business does π have showing up?

We can find reasons. One way is to look at a similar problem. Imagine dropping a disc on these lines. What’s the chance the disc falls across some line? That’s the chance that the center of the disc is less than one radius from any of the lines. What if the disc has an equal chance of landing anywhere on the floor? Then it has a probability of of crossing a line. If the radius is smaller than the distance between lines, anyway. If the radius is larger than that, the probability is 1.

Now draw a diameter line on this disc. What’s the chance that this diameter line crosses this floor line? That depends on a couple things. Whether the center of the disc is near enough a floor line. And what angle the diameter line makes with respect to the floor lines. If the diameter line is parallel the floor line there’s almost no chance. If the diameter line is perpendicular to the floor line there’s the best possible chance. But that angle might be anything.

Let me call that angle θ. The diameter line crosses the floor line if the diameter times the sine of θ is less than half the distance between floor lines. … Oh. Sine. Sine and cosine and all the trigonometry functions we get from studying circles, and how to draw triangles within circles. And this diameter-line problem looks the same as the needle problem. So that’s where π comes from.

I’m being figurative. I don’t think one can make a rigorous declaration that the π in the probability formula “comes from” this sine, any more than you can declare that the square-ness of a shape comes from any one side. But it gives a reason to believe that π belongs in the probability.

If the needle’s longer than the gap between floor lines, if , there’s still a probability that the needle crosses at least one line. It never becomes certain. No matter how long the needle is it could fall parallel to all the floor lines and miss them all. The probability is instead:

Here is the world-famous arcsecant function. That is, it’s whatever angle has as its secant the number . I don’t mean to insult you. I’m being kind to the person reading this first thing in the morning. I’m not going to try justifying this formula. You can play with numbers, though. You’ll see that if is a little bit bigger than 1, the probability is a little more than what you get if is a little smaller than 1. This is reassuring.

The exciting thing is arithmetic, though. Use the probability of a needle crossing a line, for short needles. You can re-write it as this:

L and d you can find by measuring needles and the lines. P you can estimate. Drop a needle many times over. Count how many times you drop it, and how many times it crosses a line. P is roughly the number of crossings divided by the number of needle drops. Doing this gives you a way to estimate π. This gives you something to talk about on Pi Day.

It’s a rubbish way to find π. It’s a lot of work, plus you have to sweep needles off the floor. Well, you can do it in simulation and avoid the risk of stepping on an overlooked needle. But it takes a lot of needle-drops to get good results. To be certain you’ve calculated the first two decimal points correctly requires 3,380,000 needle-drops. Yes, yes. You could get lucky and happen to hit on an estimate of 3.14 for π with fewer needle-drops. But if you were sincerely trying to calculate the digits of π this way? If you did not know what they were? You would need the three and a third million tries to be confident you had the number correct.

So this result is, as a practical matter, useless. It’s a heady concept, though. We think casually of randomness as … randomness. Unpredictability. Sometimes we will speak of the Law of Large Numbers. This is several theorems in probability. They all point to the same result. That if some event has (say) a probability of one-third of happening, then given 30 million chances, it will happen quite close to 10 million times.

This π result is another casting of the Law of Large Numbers, and of the apparent paradox that true unpredictability is itself predictable. There is no way to predict whether any one dropped needle will cross any line. It doesn’t even matter whether any one needle crosses any line. An enormous number of needles, tossed without fear or favor, will fall in ways that embed π. The same π you get from comparing the circumference of a circle to its diameter. The same π you get from looking at the arc-cosine of a negative one.

I suppose we could use this also to calculate the value of 2, but that somehow seems to touch lesser majesties.

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Thank you again for reading. All of the Fall 2019 A To Z posts should be at this link. This year’s and all past A To Z sequences should be at this link. I’ve made my picks for next week’s topics, and am fooling myself into thinking I have a rough outline for them already. But I’m still open for suggestions for the letters E through H and appreciate suggestions.

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Reading the Comics, March 14, 2019: Pi Day 2019 Edition

Some weeks there’s an obvious theme. Most weeks there’s not. But mid-March has formed a traditional theme for at least one day. I’m going to excerpt that from the rest of the week’s comics, because I’ve noticed what readership around here is like for stuff tagged “Pi Day” in mid-March. You all can do what you like with your pop-mathematics blogs.

Pi Day seems to have brought out fewer comics than in years past. The ones that were made, among the set I read, were also less on point. There was a lot of actual physical pie involved, too, suggesting the day might be escaping the realm of pop-mathematics silliness straight into pun nobody thinks about. Or maybe cartoonists just didn’t have a fresh angle this year.

John Hambrock’s The Brilliant Mind of Edison Lee shows off a nerd kind of mistake. At least one I think of as particularly nerdy. Wanting to calculate is a natural urge, especially for those who do it well. But to calculate the circumference of a pie from its diameter? What is exciting about that? More, does Grandpa recognize what a circumference is? It’s relatively easy to see the diameter of a pie. Area, also. But circumference? I’m not sure people are good at estimating the circumference of things, not by sight. You’d need a tape measure, or a similar flexible ruler, to start with and we don’t see that. Without the chance to measure it himself, Grandpa has to take the circumference (and, for that matter, diameter) at Edison Lee’s word. What would convince Grandpa of anything?

John Hambrock’s The Brilliant Mind of Edison Lee for the 14th of March, 2019. This and other essays inspired by Edison Lee can be found at this link.

For example, even if Grandpa accepted that Edison Lee had multiplied one number by 3.14 and gotten another number he might ask: how do we know pi is the same for pies of all sizes? Could a small pie’s circumference be only three times the diameter’s length, while a large pie’s is four times that? Could Edison offer an answer for why 3.14, or some nearby number, is all that interesting?

Liz Climo’s Cartoons for the 14th of March, 2019. I haven’t had reason to discuss this comic here before. This and any future essays discussing Liz Climo Cartoons should appear at this new tag.

Liz Climo’s Cartoons is an example of the second kind of strip I mentioned during my introductory paragraphs. While it’s nominally built on Pi Day, any mathematics is gone. It’s just about the pun. And, well, the fun of having a capybara around.

Mark Parisi’s Off The Mark is the most on-topic strip for the day. And the anthropomorphic numerals joke for the day, too. It’s built on there being infinitely many digits to π, which, true enough. There are also infinitely many digits to , mind; they’re just not so interesting a set. π being irrational gives us a never-ending variety of digits. It’s almost certainly normal, too. Any finite string of digits most likely appears infinitely often in this string.

Mark Parisi’s Off The Mark for the 14th of March, 2019. The essays inspired by Off The Mark should appear at this link.

We won’t ever know enough digits of π to depict all of them. But we can depict the digits we know, and many different ways. Here’s a 2015 Washington Post article with several pictures representing the digits, including some neat “random walk” ones. In those the digits are used to represent directions and distances for a thing to move, and it represents the number as this curious wispy structure. There’s amazing pictures to be made of this.

John Zakour and Scott Roberts’s Working Daze for the 15th of March, 2019. And this comic appears often enough. Working Days strips should appear in discussions at this link.

John Zakour and Scott Roberts’s Working Daze for the 15th is built more around the pie pun. I was relieved to see this. The kind of nerd jokes routinely made in Working Daze made me think it was bizarre the comic strip didn’t do a Pi Day joke. They were saving the setup.

Bill Schorr’s The Grizzwells for the 13th of March, 2019. I’ve had a few chances to mention The Grizzwells and those essays are at this link.

And last, a comic strip that I don’t think was trying to set up a Pi Day joke. But Bill Schorr’s The Grizzwells for the 13th is a routine story problem joke. But that the setup mentions pies? If this ran on the 14th I would feel confident Schorr was going for a Pi Day comic. But it didn’t, so I don’t know if Schorr was going for that or not.

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And those are the surprisingly few Pi Day 2019 comic strips. Later this week I should post, at this link, other recent mathematically-themed comic strips. Thanks for reading.

Six Or Arguably Four Things For Pi Day

I hope you’ll pardon me for being busy. I haven’t had the chance to read all the Pi Day comic strips yet today. But I’d be a fool to let the day pass without something around here. I confess I’m still not sure that Pi Day does anything lasting to encourage people to think more warmly of mathematics. But there is probably some benefit if people temporarily think more fondly of the subject. Certainly I’ll do more foolish things than to point at things and say, “pi, cool, huh?” this week alone.

I’ve got a couple of essays that discuss π some. The first noteworthy one is Calculating Pi Terribly, discussing a way to calculate the value of π using nothing but a needle, a tile floor, and a hilariously excessive amount of time. Or you can use an HTML5-and-JavaScript applet and slightly less time, and maybe even experimentally calculate the digits of π to two decimal places, if you get lucky.

Tom Toles’s Randolph Itch, 2am for the 11th of June, 2018. I’m not sure when it did first run, past that it was in 2000, but I’ve featured it at least two times before, both of those in 2015, peculiarly. So in short I have no idea how GoComics picks its reruns for this strip.

In Calculating Pi Less Terribly I showed a way to calculate π that’s … well, you see where that sentence was going. This is a method that uses an alternating series. To get π exactly correct you have to do an infinite amount of work. But if you just want π to a certain precision, all right. This will even tell you how much work you have to do. There are other formulas that will get you digits of π with less work, though, and maybe I’ll write up one of those sometime.

Dave Whamond’s Reality Check for the 27th of October, 2018. Does the weight count if the jack-o-lantern is wearing sneakers?

And the last of the relevant essays I’ve already written is an A To Z essay about normal numbers. I don’t know whether π is a normal number. No human, to the best of my knowledge, does. Well, anyone with an opinion on the matter would likely say, of course it’s normal. There’s fantastic reasons to think it is. But none of those amount to a proof it is.

Scott Hilburn’s The Argyle Sweater for the 14th of March, 2018. Also a free probability question, if you’re going to assume that every second of the year is equally likely to be the time of birth.

That’s my three items. After that I’d like to share … I don’t know whether to classify this as one or three pieces. They’re YouTube videos which a couple months ago everybody in the world was asking me if I’d seen. Now it’s your turn. I apologize if you too got this, a couple months ago, but don’t worry. You can tell people you watched and not actually do it. I’ll alibi you.

Mark Parisi’s Off The Mark for the 14th of March, 2018. Really the book seems a little short for that.

It’s a string of videos posted on youTube by 3Blue1Brown. The first lays out the matter with a neat physics problem. Imagine you have an impenetrable wall, a frictionless floor, and two blocks. One starts at rest. The other is sliding towards the first block and the wall. How many times will one thing collide with another? That is, will one block collide with another block, or will one block collide with a wall?

Michael Cavna’s Warped for the 14th of March, 2018. Yes, but have you seen Pythagoras and his golden thigh?

The answer seems like it should depend on many things. What it actually depends on is the ratio of the masses of the two blocks. If they’re the same mass, then there are three collisions. You can probably work that sequence out in your head and convince yourself it’s right. If the outer block has ten times the mass of the inner block? There’ll be 31 collisions before all the hits are done. You might work that out by hand. I did not. You will not work out what happens if the outer block has 100 times the mass of the inner block. That’ll be 314 collisions. If the outer block has 1,000 times the mass of the inner block? 3,141 collisions. You see where this is going.

John Zakour and Scott Roberts’s Working Daze for the 15th of March, 2018. No, you should never read the comments, but here, really, don’t read the comments.

The second video in the sequence explains why the digits of π turn up in this. And shows how to calculate this. You could, in principle, do this all using Newtonian mechanics. You will not live long enough to finish that, though.

Daniel Beyer’s Long Story Short for the 14th of March, 2015.

The video shows a way that saves an incredible load of work. But you save on that tedious labor by having to think harder. Part of it is making use of conservation laws, that energy and linear momentum are conserved in collisions. But part is by recasting the problem. Recast it into “phase space”. This uses points in an abstract space to represent different configurations of a system. Like, how fast blocks are moving, and in what direction. The recasting of the problem turns something that’s impossibly tedious into something that’s merely … well, it’s still a bit tedious. But it’s much less hard work. And it’s a good chance to show off you remember the Inscribed Angle Theorem. You do remember the Inscribed Angle Theorem, don’t you? The video will catch you up. It’s a good show of how phase spaces can make physics problems so much more manageable.

John Hambrock’s The Brilliant Mind of Edison Lee for the 14th of March, 2016. The strip is like this a lot.

The third video recasts the problem yet again. In this form, it’s about rays of light reflecting between mirrors. And this is a great recasting. That blocks bouncing off each other and walls should have anything to do with light hitting mirrors seems ridiculous. But set out your phase space, and look hard at what collisions and reflections are like, and you see the resemblance. The sort of trick used to make counting reflections easy turns up often in phase spaces. It also turns up in physics problems on toruses, doughnut shapes. You might ask when do we ever do anything on a doughnut shape. Well, real physical doughnuts, not so much. But problems where there are two independent quantities, and both quantities are periodic? There’s a torus lurking in there. There might be a phase space using that shape, and making your life easier by doing so.

Scott Hilburn’s The Argyle Sweater for the 14th of March, 2017. And while the strip is true, arguably, 2 goes on forever also; it’s just not very interesting how it does.

That’s my promised four or maybe six items. Pardon, please, now, as I do need to get back to reading the comics.

Reading the Comics, January 12, 2019: A Edition

As I said Sunday, last week was a slow one for mathematically-themed comic strips. Here’s the second half of them. They’re not tightly on point. But that’s all right. They all have titles starting with ‘A’. I mean if you ignore the article ‘the’, the way we usually do when alphabetizing titles.

Tony Cochran’s Agnes for the 11th is basically a name-drop of mathematics. The joke would be unchanged if the teacher asked Agnes to circle all the adjectives in a sentence, or something like that. But there are historically links between religious thinking and mathematics. The Pythagoreans, for example, always a great and incredible starting point for any mathematical topic or just some preposterous jokes that might have nothing to do with their reality, were at least as much a religious and philosophical cult. For a long while in the Western tradition, the people with the time and training to do advanced mathematics work were often working for the church. Even as people were more able to specialize, a mystic streak remained. It’s easy to understand why. Mathematics promises to speak about things that are universally true. It encourages thinking about the infinite. It encourages thinking about the infinitely tiny. It courts paradoxes as difficult as any religious Mystery. It’s easy to snark at someone who takes numerology seriously. But I’m not sure the impulse that sees magic in arithmetic is different to the one that sees something supernatural in a “transfinite” item.

Tony Cochran’s Agnes for the 11th of January, 2019. I’m always glad to have the chance to write about Agnes, and you can see things I’ve written about it at this link.

Scott Hilburn’s The Argyle Sweater for the 11th is another mistimed Pi Day joke. π is, famously, an irrational number. But so is every number, except for a handful of strange ones that we’ve happened to find interesting. That π should go on and on follows from what an irrational number means. It’s a bit surprising the 4 didn’t know all this before they married.

Scott Hilburn’s The Argyle Sweater for the 11th of January, 2019. It’s not quite the most common strip mentioned here. But you can find other topics raised by The Argyle Sweater at this link.

I appreciate the secondary joke that the marriage counselor is a “Hugh Jripov”, and the counselor’s being a ripoff is signaled by being a ÷ sign. It suggests that maybe successful reconciliation isn’t an option. I’m curious why the letters ‘POV’ are doubled, in the diploma there. In a strip with tighter drafting I’d think it was suggesting the way a glass frame will distort an image. But Hilburn draws much more loosely than that. I don’t know if it means anything.

Mark Anderson’s Andertoons for the 12th of January, 2019. There’s more essays with Andertoons at this link.

Mark Anderson’s Andertoons for the 12th is the Mark Anderson’s Andertoons for the essay. I’m so relieved to have a regular stream of these again. The teacher thinks Wavehead doesn’t need to annotate his work. And maybe so. But writing down thoughts about a problem is often good practice. If you don’t know what to do, or you aren’t sure how to do what you want? Absolutely write down notes. List the things you’d want to do. Or things you’d want to know. Ways you could check your answer. Ways that you might work similar problems. Easier problems that resemble the one you want to do. You find answers by thinking about what you know, and the implications of what you know. Writing these thoughts out encourages you to find interesting true things.

And this was too marginal a mention of mathematics even for me, even on a slow week. But Georgia Dunn’s Breaking Cat News for the 12th has a cat having a nightmare about mathematics class. And it’s a fun comic strip that I’d like people to notice more.

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And that’s as many comics as I have to talk about from last week. Sunday, I should have another Reading the Comics post and it’ll be at this link.

Reading the Comics, January 9, 2018: I Go On About Johnny Appleseed Edition

This was a slow week for mathematically-themed comic strips. Such things happen. I put together a half-dozen that see on-topic enough to talk about, but I stretched to do it. You’ll see.

Mark Anderson’s Andertoons for the 6th mentions addition as one of the things you learn in an average day of elementary school. I can’t help noticing also the mention of Johnny Appleseed, who’s got a weird place in my heart as he and I share a birthday. He got to it first. Although Johnny Appleseed — John Champan — is legendary for scattering apple seeds, that’s not what he mostly did. He would more often grow apple-tree nurseries, from which settlers could buy plants and demonstrate they were “improving” their plots. He was also committed to spreading the word of Emanuel Swedenborg’s New Church, one of those religious movements that you somehow don’t hear about. But there was this like 200-year-long stretch where a particular kind of idiosyncratic thinker was Swedenborgian, or at least influenced by that. I don’t know offhand of any important Swedenborgian mathematicians, I admit, but I’m glad to hear if someone has news.

Mark Anderson’s Andertoons for the 6th of January, 2019. Andertoons often appears in these essays. You can see the proof of that Andertoons claim at this link.

Justin Thompson’s MythTickle rerun for the 9th mentions “algebra” as something so dreadful that even being middle-aged is preferable. Everyone has their own tastes, yes, although it would be the same joke if it were “gym class” or something. (I suppose that’s not one word. “Dodgeball” would do, but I never remember playing it. It exists just as a legendarily feared activity, to me.) Granting, though, that I had a terrible time with the introduction to algebra class I had in middle school.

Justin Thompson’s MythTickle rerun for the 9th of January, 2019. MythTickle has only barely appeared before in these essays. You can see the proof of that MythTickle claim at this link.

Tom Wilson’s Ziggy for the 9th is a very early Pi Day joke, so, there’s that. There’s not much reason a take-a-number dispenser couldn’t give out π, or other non-integer numbers. What the numbers are doesn’t matter. It’s just that the dispensed numbers need to be in order. It should be helpful if there’s a clear idea how uniformly spaced the numbers are, so there’s some idea how long a wait to expect between the currently-serving number and whatever number you’ve got. But that only helps if you have a fair idea of how long an order should on average take.

Tom Wilson’s Ziggy for the 9th of January, 2019. Ziggy has turned up once or twice in these essays. You can see the proof of that Ziggy claim at this link.

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I’ll close out last week’s comics soon. The next Reading the Comics post, like all the earlier ones, should be at this link.

Reading the Comics, December 5, 2018: December 5, 2018 Edition

And then I noticed there were a bunch of comic strips with some kind of mathematical theme on the same day. Always fun when that happens.

Bill Holbrook’s On The Fastrack uses one of Holbrook’s common motifs. That’s the depicting as literal some common metaphor. in this case it’s “massaging the numbers”, which might seem not strictly mathematics. But while numbers are interesting, they’re also useful. To be useful they must connect to something we want to know. They need context. That context is always something of human judgement. If the context seems inappropriate to the listener, she thinks the presenter is massaging the numbers. If the context seems fine, we trust the numbers as showing something truth.

Bill Holbrook’s On The Fastrack for the 5th of December, 2018. Essays inspired by On The Fastrack appear at this link.

Scott Hilburn’s The Argyle Sweater is a seasonal pun that couldn’t wait for a day closer to Christmas. I’m a little curious why not. It would be the same joke with any subject, certainly. The strip did make me wonder if Ebeneezer Scrooge, in-universe, might have taken calculus. This lead me to see that it’s a bit vague what, precisely, Scrooge, or Scrooge-and-Marley, did. The movies are glad to position him as having a warehouse, and importing and exporting things, and making and collecting on loans and whatnot. These are all trades that mathematicians would like to think benefit from knowing advanced mathematics. The logic of making loans implies attention be paid to compounding interest, risks, and expectation values, as well as projecting cash-flow a fair bit into the future. But in the original text he doesn’t make any stated loans, and the only warehouse anyone enters is Fezziwig’s. Well, the Scrooge and Marley sign stands “above the warehouse door”, but we only ever go in to the counting-house. And yes, what Scrooge does besides gather money and misery is irrelevant to the setting of the story.

Scott Hilburn’s The Argyle Sweater for the 5th of December, 2018. Some of the many times I’ve talked about The Argyle Sweater appear at this link.

Teresa Burritt’s Dadaist strip Frog Applause uses knowledge of mathematics as an emblem of intelligence. “Multivariate analysis” is a term of art from statistics. It’s about measuring how one variable changes depending on two or more other variables. The goal is obvious: we know there are many things that influence anything of interest. Can we find what things have the strongest effects? The weakest effects? There are several ways we might mean “strongest” effect, too. It might mean that a small change in the independent variable produces a big change in the dependent one. Or it might mean that there’s very little noise, that a change in the independent variable produces a reliable change in the dependent one. Or we might have several variables that are difficult to measure precisely on their own, but with a combination that’s noticeable. The basic calculations for this look a lot like those for single-variable analysis. But there’s much more calculation. It’s more tedious, at least. My reading suggests that multivariate analysis didn’t develop much until there were computers cheap enough to do the calculations. Might be coincidence, though. Many machine-learning techniques can be described as multivariate analysis problems.

Teresa Burritt’s Frog Applause for the 5th of December, 2018. Essays with reason to mention Frog Applause should be at this link.

Greg Evans’s Luann Againn is a Pi Day joke from before the time when Pi Day was a thing. Brad’s magazine flipping like that is an unusual bit of throwaway background humor for the comic strip.

Greg Evans’s Luann Againn for the 5th of December, 2018. This originally ran the 5th of December, 1990. Essays which mention Luann, current-day or 1990-vintage rerun, appear at this link.

Doug Savage’s Savage Chickens is a bunch of shape jokes. Since I was talking about tiling the plane so recently the rhombus seemed on-point enough. I’m think the irregular heptagon shown here won’t tile the plane. But given how much it turns out I didn’t know, I wouldn’t want to commit to that.

Doug Savage’s Savage Chickens for the 5th of December, 2018. Essays that mention Savage Chickens are at this link.

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I’m working hard on a latter ‘X’ essay for my Fall 2018 Mathematics A To Z glossary. That should appear on Friday. And there should be another Reading the Comics post later this week, at this link.

Reading the Comics, December 4, 2018: Christmas Specials Edition

This installment took longer to write than you’d figure, because it’s the time of year we’re watching a lot of mostly Rankin/Bass Christmas specials around here. So I have to squeeze words out in-between baffling moments of animation and, like, arguing whether there’s any possibility that Jack Frost was not meant to be a Groundhog Day special that got rewritten to Christmas because the networks weren’t having it otherwise.

Graham Nolan’s Sunshine State for the 3rd is a misplaced Pi Day strip. I did check the copyright to see if it might be a rerun from when it was more seasonal.

Graham Nolan’s Sunshine State for the 3rd of December, 2018. This and other essays mentioning Sunshine State should be at this link. Or will be someday; it’s a new tag. Yeah, Paul’s so smart he almost knows the difference between it’s and its.

Jeffrey Caulfield and Brian Ponshock’s Yaffle for the 3rd is the anthropomorphic numerals joke for the week. … You know, I’ve always wondered in this sort of setting, what are two-digit numbers like? I mean, what’s the difference between a twelve and a one-and-two just standing near one another? How do people recognize a solitary number? This is a darned silly thing to wonder so there’s probably a good web comic about it.

Jeffrey Caulfield and Brian Ponshock’s Yaffle for the 3rd of December, 2018. Essays inspired by Yaffle should appear at this link. It’s also a new tag, so don’t go worrying that there’s only this one essay there yet.

John Hambrock’s The Brilliant Mind of Edison Lee for the 4th has Edison forecast the outcome of a basketball game. I can’t imagine anyone really believing in forecasting the outcome, though. The elements of forecasting a sporting event are plausible enough. We can suppose a game to be a string of events. Each of them has possible outcomes. Some of them score points. Some block the other team’s score. Some cause control of the ball (or whatever makes scoring possible) to change teams. Some take a player out, for a while or for the rest of the game. So it’s possible to run through a simulated game. If you know well enough how the people playing do various things? How they’re likely to respond to different states of things? You could certainly simulate that.

John Hambrock’s The Brilliant Mind of Edison Lee for the 4th of December, 2018. More ideas raised by Edison Lee I discuss at this link. Also it turns out Edison’s friend here is named Harley, which I mention so I have an easier time finding his name next time I need to refer to this strip. This will not work.

But all sorts of crazy things will happen, one game or another. Run the same simulation again, with different random numbers. The final score will likely be different. The course of action certainly will. Run the same simulation many times over. Vary it a little; what happens if the best player is a little worse than average? A little better? What if the referees make a lot of mistakes? What if the weather affects the outcome? What if the weather is a little different? So each possible outcome of the sporting event has some chance. We have a distribution of the possible results. We can judge an expected value, and what the range of likely outcomes is. This demands a lot of data about the players, though. Edison Lee can have it, I suppose. The premise of the strip is that he’s a genius of unlimited competence. It would be more likely to expect for college and professional teams.

Brian Basset’s Red and Rover for the 4th of December, 2018. And more Red and Rover discussions are at this link.

Brian Basset’s Red and Rover for the 4th uses arithmetic as the homework to get torn up. I’m not sure it’s just a cameo appearance. It makes a difference to the joke as told that there’s division and long division, after all. But it could really be any subject.

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I’m figuring to get to the letter ‘W’ in my Fall 2018 Mathematics A To Z glossary for Tuesday. Reading the Comics posts this week. And I also figure there should be two more When posted, they’ll be at this link.

Reading the Comics, November 5, 2018: November 5, 2018 Edition

This past week included one of those odd days that’s so busy I get a column’s worth of topics from a single day’s reading. And there was another strip (the Cow and Boy rerun) which I might have roped in had the rest of the week been dead. The Motley rerun might have made the cut too, for a reference to .

Jason Chatfield’s Ginger Meggs for the 5th is a joke about resisting the story problem. I’m surprised by the particulars of this question. Turning an arithmetic problem into counts of some number of particular things is common enough and has a respectable history. But slices of broccoli quiche? I’m distracted by the choice, and I like quiche. It’s a weird thing for a kid to have, and a weird amount for anybody to have.

Jason Chatfield’s Ginger Meggs for the 5th of November, 2018. I’m of the age cohort to remember Real Men Don’t Eat Quiche being a book people had for some reason. Also not understanding why “real men” would not eat quiche. If you named the same dish “Cheddar Bacon Pie” you’d have men lined up for a quarter-mile to get it. Anyway, it took me too long to work out but I think the teacher’s name is Mr Crackett? Cast lists, cartoonists. We need cast lists on your comic’s About pages.

JC Duffy’s Lug Nuts for the 5th uses mathematics as a shorthand for intelligence. And it particularly uses π as shorthand for mathematics. There’s a lot of compressed concepts put into this. I shouldn’t be surprised if it’s rerun come mid-March.

JC Duffy’s Lug Nuts for the 5th of November, 2018. OK, some of these strips I don’t need a cast list for.

Tom Toles’s Randolph Itch, 2 am for the 5th I’ve highlighted before. It’s the pie chart joke. It will never stop amusing me, but I suppose I should take Randolph Itch, 2 am out of my rotation of comics I read to include here.

Tom Toles’s Randolph Itch, 2 am for the 5th of November, 2018. I never get to presentations like this. It’s always someone explaining the new phone system.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 5th is a logic puzzle joke. And a set theory joke. Dad is trying to argue he can’t be surprised by his gift because it’ll belong to one of two sets of things. And he receives nothing. This ought to defy his expectations, if we think of “nothing” as being “the empty set”. The empty set is an indispensable part of set theory. It’s a set that has no elements, has nothing in it. Then suppose we talk about what it means for one set to be contained in another. Take what seems like an uncontroversial definition: set A is contained in set B if there’s nothing in A which is not also in B. Then the empty set is contained inside every set. So Dad, having supposed that he can’t be surprised, since he’d receive either something that is “socks” or something that is “not-socks”, does get surprised. He gets the one thing that is both “socks” and “not-socks” simultaneously.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 5th of November, 2018. I may have mentioned. So my partner in Modern Physics Lab one time figured to organize his dorm room by sorting everything in it into two piles, “pair of socks” and “not a pair of socks”. I asked him how he’d classify two socks that, while mismatched, were bundled together. He informed me that he hated me.

I hate to pull this move a third time in one week (see here and here), but the logic of the joke doesn’t work for me. I’ll go along with “nothing” as being “the empty set” for these purposes. And I’ll accept that “nothing” is definitely “not-socks”. But to say that “nothing” is also “socks” is … weird, unless you are putting it in the language of set theory. I think the joke would be saved if it were more clearly established that Dad should be expecting some definite thing, so that no-thing would defy all expectations.

“Nothing” is a difficult subject to treat logically. I have been exposed a bit to the thinking of professional philosophers on the subject. Not enough that I feel I could say something non-stupid about the subject. But enough to say that yeah, they’re right, we have a really hard time describing “nothing”. The null set is better behaved. I suppose that’s because logicians have been able to tame it and give it some clearly defined properties.

Mike Shiell’s The Wandering Melon for the 5th of November, 2018. I am curious whether this is meant to be the same lottery winner who in August got struck by lightning. It would make the torn, singed check make more direct sense. But what are the odds someone wins the lottery, gets hit by lightning, and then eaten by a crocodile? … Ah well, at least nothing worse is going to happen to him.

Mike Shiell’s The Wandering Melon for the 5th felt like a rerun to me. It wasn’t. But Shiell did do a variation on this joke in August. Both are built on the same whimsy of probability. It’s unlikely one will win a lottery. It’s unlikely one will die in a particular and bizarre way. What are the odds someone would have both things happen to them?

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This and every Reading the Comics post should be at this link. Essays that include Ginger Meggs are at this link. Essays in which I discuss Lug Nuts are at this link. Essays mentioning Randolph Itch, 2 am, should be at this link. The many essays with a mention of Saturday Morning Breakfast Cereal are at this link. And essays where I’m inspired by something in The Wandering Melon should be at this link. And, what the heck, when I really discuss Cow and Boy it’s at this link. Real discussions of Motley are at this link. And my Fall 2018 Mathematics A-To-Z averages two new posts a week, now and through December. Thanks again for reading.

Reading the Comics, March 17, 2018: Pi Day 2018 Edition

So today I am trying out including images for all the mathematically-themed comic strips here. This is because of my discovery that some links even on GoComics.com vanish without warning. I’m curious how long I can keep doing this. Not for legal reasons. Including comics for the purpose of an educational essay about topics raised by the strips is almost the most fair use imaginable. Just because it’s a hassle copying the images and putting them up on WordPress.com and that’s even before I think about how much image space I have there. We’ll see. I might try to figure out a better scheme.

Also in this batch of comics are the various Pi Day strips. There was a healthy number of mathematically-themed comics on the 14th of March. Many of those were just coincidence, though, with no Pi content. I’ll group the Pi Day strips together.

Tom Batiuk’s Funky Winkerbean for the 2nd of April, 1972 and rerun the 11th of March, 2018. Maybe I’m just overbalancing for the depression porn that Funky Winkerbean has become, but I find this a funny bordering-on-existential joke.

Tom Batiuk’s Funky Winkerbean for the 2nd of April, 1972 is, I think, the first appearance of Funky Winkerbean around here. Comics Kingdom just started running the strip, as well as Bud Blake’s Tiger and Bill Hoest’s Lockhorns, from the beginning as part of its Vintage Comics roster. And this strip really belonged in Sunday’s essay, but I noticed the vintage comics only after that installment went to press. Anyway, this strip — possibly the first Sunday Funky Winkerbean — plays off a then-contemporary fear of people being reduced to numbers in the face of a computerized society. If you can imagine people ever worrying about something like that. The early 1970s were a time in American society when people first paid attention to the existence of, like, credit reporting agencies. Just what they did and how they did it drew a lot of critical examination. Josh Lauer’s recently published Creditworthy: a History of Consumer Surveillance and Financial Identity in America gets into this.

Bob Scott’s Bear With Me for the 14th of March, 2018. Every conversation with a high-need, low-self-esteem friend.

Bob Scott’s Bear With Me for the 14th sees Molly struggling with failure on a mathematics test. Could be any subject and the story would go as well, but I suppose mathematics gets a connotation of the subject everybody has to study for, even the geniuses. (The strip used to be called Molly and the Bear. In either name this seems to be the first time I’ve tagged it, although I only started tagging strips by name recently.)

Bud Fisher’s Mutt and Jeff rerun for the 14th of March, 2018. The comic strip ended the 26th of June, 1983 — I remember the announcement of its ending in the (Perth Amboy) News-Tribune, our evening paper, and thinking it seemed illicit that an ancient comic strip like that could end. It was a few months from being 76 years old then.

Bud Fisher’s Mutt and Jeff rerun for the 14th is a rerun from sometime in 1952. I’m tickled by the problem of figuring out how many times Fisher and his uncredited assistants drew Mutt and Jeff. Mutt saying that the boss “drew us 14,436 times” is the number of days in 45 years, so that makes sense if he’s counting the number of strips drawn. The number of times that Mutt and Jeff were drawn is … probably impossible to calculate. There’s so many panels each strip, especially going back to earlier and earlier times. And how many panels don’t have Mutt or don’t have Jeff or don’t have either in them? Jeff didn’t appear in the strip until March of 1908, for example, four months after the comic began. (With a different title, so the comic wasn’t just dangling loose all that while.)

Doug Savage’s Savage Chickens for the 14th of March, 2018. Yeah, William Playfair invented all these too.

Doug Savage’s Savage Chickens for the 14th is a collection of charts. Not all pie charts. And yes, it ran the 14th but avoids the pun it could make. I really like the tart charts, myself.

And now for the Pi Day strips proper.

Scott Hilburn’s The Argyle Sweater for the 14th of March, 2018. Also a free probability question, if you’re going to assume that every second of the year is equally likely to be the time of birth.

Scott Hilburn’s The Argyle Sweater for the 14th starts the Pi Day off, of course, with a pun and some extension of what makes 3/14 get its attention. And until Hilburn brought it up I’d never thought about the zodiac sign for someone born the 14th of March, so that’s something.

Mark Parisi’s Off The Mark for the 14th of March, 2018. Really the book seems a little short for that.

Mark Parisi’s Off The Mark for the 14th riffs on one of the interesting features of π, that it’s an irrational number. Well, that its decimal representation goes on forever. Rational numbers do that too, yes, but they all end in the infinite repetition of finitely many digits. And for a lot of them, that digit is ‘0’. Irrational numbers keep going on with more complicated patterns. π sure seems like it’s a normal number. So we could expect that any finite string of digits appears somewhere in its decimal expansion. This would include a string of digits that encodes any story you like, The Neverending Story included. This does not mean we might ever find where that string is.

Michael Cavna’s Warped for the 14th of March, 2018. Yes, but have you seen Pythagoras and his golden thigh?

Michael Cavna’s Warped for the 14th combines the two major joke threads for Pi Day. Specifically naming Archimedes is a good choice. One of the many things Archimedes is famous for is finding an approximation for π. He’d worked out that π has to be larger than 3¹⁰/₇₁ but smaller than 3 ¹/₇. Archimedes used an ingenious approach: we might not know the precise area of a circle given only its radius. But we can know the area of a triangle if we know the lengths of its legs. And we can draw a series of triangles that are enclosed by a circle. The area of the circle has to be larger than the sum of the areas of those triangles. We can draw a series of triangles that enclose a circle. The area of the circle has to be less than the sum of the areas of those triangles. If we use a few triangles these bounds are going to be very loose. If we use a lot of triangles these bounds can be tight. In principle, we could make the bounds as close together as we could possibly need. We can see this, now, as a forerunner to calculus. They didn’t see it as such at the time, though. And it’s a demonstration of what amazing results can be found, even without calculus, but with clever specific reasoning. Here’s a run-through of the process.

John Zakour and Scott Roberts’s Working Daze for the 15th of March, 2018. No, you should never read the comments, but here, really, don’t read the comments.

John Zakour and Scott Roberts’s Working Daze for the 15th is a response to Dr Stephen Hawking’s death. The coincidence that he did die on the 14th of March made for an irresistibly interesting bit of trivia. Zakour and Roberts could get there first, thanks to working on a web comic and being quick on the draw. (I’m curious whether they replaced a strip that was ready to go for the 15th, or whether they normally work one day ahead of publication. It’s an exciting but dangerous way to go.)

And My Pi Day Stuff

The 14th of March offers many things. A chance for calendar nerds to get all excited about the meaning of “ides”. A chance to bring out Pi-related content on mathematics blogs. I’ll take advantage of the latter. There’s not a lot in public dispute about the ides of March. The ides of February, now, that I’m not sure I can talk about coherently. But, for Pi:

• The End 2016 Mathematics A To Z: Normal Numbers which is relevant because π is probably a normal number. We don’t know, but it would be really weird if it weren’t. Normal numbers are weird, but most numbers are normal.
• Calculating Pi Terribly was my first, big, and basically sour essay about π. It describes the Buffon needle drop experiment, which is a real experiment you could do with actual physical objects if you wanted to eventually, someday, calculate the digits of π. You should use basically any other approach before this if you actually need to know them.
• Calculating Pi Less Terribly is a follow-up, about finding the digits of π using way less work. It gets into alternating series, which are mathematically interesting enough and very useful.

Enjoy, I hope!

Reading the Comics, June 17, 2017: Icons Of Mathematics Edition

Comic Strip Master Command just barely missed being busy enough for me to split the week’s edition. Fine for them, I suppose, although it means I’m going to have to scramble together something for the Tuesday or the Thursday posting slot. Ah well. As befits the comics, there’s a fair bit of mathematics as an icon in the past week’s selections. So let’s discuss.

Mark Anderson’s Andertoons for the 11th is our Mark Anderson’s Andertoons for this essay. Kind of a relief to have that in right away. And while the cartoon shows a real disaster of a student at the chalkboard, there is some truth to the caption. Ruling out plausible-looking wrong answers is progress, usually. So is coming up with plausible-looking answers to work out whether they’re right or wrong. The troubling part here, I’d say, is that the kid came up with pretty poor guesses about what the answer might be. He ought to be able to guess that it’s got to be an odd number, and has to be less than 10, and really ought to be less than 7. If you spot that then you can’t make more than two wrong guesses.

Patrick J Marrin’s Francis for the 12th starts with what sounds like a logical paradox, about whether the Pope could make an infallibly true statement that he was not infallible. Really it sounds like a bit of nonsense. But the limits of what we can know about a logical system will often involve questions of this form. We ask whether something can prove whether it is provable, for example, and come up with a rigorous answer. So that’s the mathematical content which justifies my including this strip here.

Niklas Eriksson’s Carpe Diem for the 13th of June, 2017. Yes, yes, it’s easy to get people excited for the Revolution, but it’ll come to a halt when someone asks about how they get the groceries afterwards.

Niklas Eriksson’s Carpe Diem for the 13th is a traditional use of the blackboard full of mathematics as symbolic of intelligence. Of course ‘E = mc²‘ gets in there. I’m surprised that both π and 3.14 do, too, for as little as we see on the board.

Mark Anderson’s Andertoons for the 14th is a nice bit of reassurance. Maybe the cartoonist was worried this would be a split-week edition. The kid seems to be the same one as the 11th, but the teacher looks different. Anyway there’s a lot you can tell about shapes from their perimeter alone. The one which most startles me comes up in calculus: by doing the right calculation about the lengths and directions of the edge of a shape you can tell how much area is inside the shape. There’s a lot of stuff in this field — multivariable calculus — that’s about swapping between “stuff you know about the boundary of a shape” and “stuff you know about the interior of the shape”. And finding area from tracing the boundary is one of them. It’s still glorious.

Samson’s Dark Side Of The Horse for the 14th is a counting-sheep joke and a Pi Day joke. I suspect the digits of π would be horrible for lulling one to sleep, though. They lack the just-enough-order that something needs for a semiconscious mind to drift off. Horace would probably be better off working out Collatz sequences.

Dana Simpson’s Phoebe and her Unicorn for the 14th mentions mathematics as iconic of what you do at school. Book reports also make the cut.

Dan Barry’s Flash Gordon for the 31st of July, 1962, rerun the 16th of June, 2017. I am impressed that Dr Zarkov can make a TV set capable of viewing alternate universes. I still literally do not know how it is possible that we have sound for our new TV set, and I labelled and connected every single wire in the thing. Oh, wouldn’t it be a kick if Dr Zarkov has the picture from one alternate universe but the sound from a slightly different other one?

Dan Barry’s Flash Gordon for the 31st of July, 1962 and rerun the 16th I’m including just because I love the old-fashioned image of a mathematician in Professor Quita here. At this point in the comic strip’s run it was set in the far-distant future year of 1972, and the action here is on one of the busy multinational giant space stations. Flash himself is just back from Venus where he’d set up some dolphins as assistants to a fish-farming operation helping to feed that world and ours. And for all that early-60s futurism look at that gorgeous old adding machine he’s still got. (Professor Quinta’s discovery is a way to peer into alternate universes, according to the next day’s strip. I’m kind of hoping this means they’re going to spend a week reading Buck Rogers.)

Reading the Comics, May 31, 2017: Feast Week Edition

You know we’re getting near the end of the (United States) school year when Comic Strip Master Command orders everyone to clear out their mathematics jokes. I’m assuming that’s what happened here. Or else a lot of cartoonists had word problems on their minds eight weeks ago. Also eight weeks ago plus whenever they originally drew the comics, for those that are deep in reruns. It was busy enough to split this week’s load into two pieces and might have been worth splitting into three, if I thought I had publishing dates free for all that.

Larry Wright’s Motley Classics for the 28th of May, a rerun from 1989, is a joke about using algebra. Occasionally mathematicians try to use the the ability of people to catch things in midair as evidence of the sorts of differential equations solution that we all can do, if imperfectly, in our heads. But I’m not aware of evidence that anyone does anything that sophisticated. I would be stunned if we didn’t really work by a process of making a guess of where the thing should be and refining it as time allows, with experience helping us make better guesses. There’s good stuff to learn in modeling how to catch stuff, though.

Michael Jantze’s The Norm Classics rerun for the 28th opines about why in algebra you had to not just have an answer but explain why that was the answer. I suppose mathematicians get trained to stop thinking about individual problems and instead look to classes of problems. Is it possible to work out a scheme that works for many cases instead of one? If it isn’t, can we at least say something interesting about why it’s not? And perhaps that’s part of what makes algebra classes hard. To think about a collection of things is usually harder than to think about one, and maybe instructors aren’t always clear about how to turn the specific into the general.

Also I want to say some very good words about Jantze’s graphical design. The mock textbook cover for the title panel on the left is so spot-on for a particular era in mathematics textbooks it’s uncanny. The all-caps Helvetica, the use of two slightly different tans, the minimalist cover art … I know shelves stuffed full in the university mathematics library where every book looks like that. Plus, “[Mathematics Thing] And Their Applications” is one of the roughly four standard approved mathematics book titles. He paid good attention to his references.

Gary Wise and Lance Aldrich’s Real Life Adventures for the 28th deploys a big old whiteboard full of equations for the “secret” of the universe. This makes a neat change from finding the “meaning” of the universe, or of life. The equations themselves look mostly like gibberish to me, but Wise and Aldrich make good uses of their symbols. The symbol , a vector-valued quantity named B, turns up a lot. This symbol we often use to represent magnetic flux. The B without a little arrow above it would represent the intensity of the magnetic field. Similarly an turns up. This we often use for magnetic field strength. While I didn’t spot a — electric field — which would be the natural partner to all this, there are plenty of bare E symbols. Those would represent electric potential. And many of the other symbols are what would naturally turn up if you were trying to model how something is tossed around by a magnetic field. Q, for example, is often the electric charge. ω is a common symbol for how fast an electromagnetic wave oscillates. (It’s not the frequency, but it’s related to the frequency.) The uses of symbols is consistent enough, in fact, I wonder if Wise and Aldrich did use a legitimate sprawl of equations and I’m missing the referenced problem.

John Graziano’s Ripley’s Believe It Or Not for the 28th mentions how many symbols are needed to write out the numbers from 1 to 100. Is this properly mathematics? … Oh, who knows. It’s just neat to know.

Mark O’Hare’s Citizen Dog rerun for the 29th has the dog Fergus struggle against a word problem. Ordinary setup and everything, but I love the way O’Hare draws Fergus in that outfit and thinking hard.

The Eric the Circle rerun for the 29th by ACE10203040 is a mistimed Pi Day joke.

Bill Amend’s FoxTrot Classicfor the 31st, a rerun from the 7th of June, 2006, shows the conflation of “genius” and “good at mathematics” in everyday use. Amend has picked a quixotic but in-character thing for Jason Fox to try doing. Euclid’s Fifth Postulate is one of the classic obsessions of mathematicians throughout history. Euclid admitted the thing — a confusing-reading mess of propositions — as a postulate because … well, there’s interesting geometry you can’t do without it, and there doesn’t seem any way to prove it from the rest of his geometric postulates. So it must be assumed to be true.

There isn’t a way to prove it from the rest of the geometric postulates, but it took mathematicians over two thousand years of work at that to be convinced of the fact. But I know I went through a time of wanting to try finding a proof myself. It was a mercifully short-lived time that ended in my humbly understanding that as smart as I figured I was, I wasn’t that smart. We can suppose Euclid’s Fifth Postulate to be false and get interesting geometries out of that, particularly the geometries of the surface of the sphere, and the geometry of general relativity. Jason will surely sometime learn.

Reading the Comics, March 18, 2017: Pi Day Edition

No surprise what the recurring theme for this set of mathematics-mentioning comic strips is. Look at the date range. But here goes.

Henry Scarpelli and Craig Boldman’s Archie rerun for the 13th uses algebra as the thing that will stun a class into silence. I know the silence. As a grad student you get whole minutes of instructions on how to teach a course before being sent out as recitation section leader for some professor. And what you do get told is the importance of asking students their thoughts and their ideas. This maybe works in courses that are obviously friendly to opinions or partially formed ideas. But in Freshman Calculus? It’s just deadly. Even if you can draw someone into offering an idea how we might start calculating a limit (say), they’re either going to be exactly right or they’re going to need a lot of help coaxing the idea into something usable. I’d like to have more chatty classes, but some subjects are just hard to chat about.

Henry Scarpelli and Craig Boldman’s Archie rerun for the 13th of March, 2017. I didn’t know the mathematics teacher’s name and suppose that “Flutesnoot” is as plausible as anything. Anyway, I admire his ability to stand in front of a dead-silent class. The stage fright the scenario produces is powerful. At least when I was taught how to teach we got nothing about stage presence or how to remain confident during awkward pauses. What I know I learned from a half-year Drama course in high school.

Steve Skelton’s 2 Cows And A Chicken for the 13th includes some casual talk about probability. As normally happens, they figure the chances are about 50-50. I think that’s a default estimate of the probability of something. If you have no evidence to suppose one outcome is more likely than the other, then that is a reason to suppose the chance of something is 50 percent. This is the Bayesian approach to probability, in which we rate things as more or less likely based on what information we have about how often they turn out. It’s a practical way of saying what we mean by the probability of something. It’s terrible if we don’t have much reliable information, though. We need to fall back on reasoning about what is likely and what is not to save us in that case.

Scott Hilburn’s The Argyle Sweater lead off the Pi Day jokes with an anthropomorphic numerals panel. This is because I read most of the daily comics in alphabetical order by title. It is also because The Argyle Sweater is The Argyle Sweater. Among π’s famous traits is that it goes on forever, in decimal representations, yes. That’s not by itself extraordinary; dull numbers like one-third do that too. (Arguably, even a number like ‘2’ does, if you write all the zeroes in past the decimal point.) π gets to be interesting because it goes on forever without repeating, and without having a pattern easily describable. Also because it’s probably a normal number but we don’t actually know that for sure yet.

Mark Parisi’s Off The Mark panel for the 14th is another anthropomorphic numerals joke and nearly the same joke as above. The answer, dear numeral, is “chained tweets”. I do not know that there’s a Twitter bot posting the digits of π in an enormous chained Twitter feed. But there’s a Twitter bot posting the digits of π in an enormous chained Twitter feed. If there isn’t, there is now.

John Zakour and Scott Roberts’s Working Daze for the 14th is your basic Pi Day Wordplay panel. I think there were a few more along these lines but I didn’t record all of them. This strip will serve for them all, since it’s drawn from an appealing camera angle to give the joke life.

Dave Blazek’s Loose Parts for the 14th is a mathematics wordplay panel but it hasn’t got anything to do with π. I suspect he lost track of what days he was working on, back six or so weeks when his deadline arrived.

Keith Tutt and Daniel Saunders’s Lard’s World Peace Tips for the 15th is some sort of joke about the probability of the world being like what it seems to be. I’m not sure precisely what anyone is hoping to express here or how it ties in to world peace. But the world does seem to be extremely well described by techniques that suppose it to be random and unpredictable in detail. It is extremely well predictable in the main, which shows something weird about the workings of the world. It seems to be doing all right for itself.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 15th is built on the staggering idea that the Earth might be the only place with life in the universe. The cosmos is a good stand-in for infinitely large things. It might be better as a way to understand the infinitely large than actual infinity would be. Somehow thinking of the number of stars (or whatnot) in the universe and writing out a representable number inspires an understanding for bigness that the word “infinity” or the symbols we have for it somehow don’t seem to, at least to me.

Mikael Wulff and Anders Morgenthaler’s TruthFacts for the 17th gives us valuable information about how long ahead of time the comic strips are working. Arithmetic is probably the easiest thing to use if one needs an example of a fact. But even “2 + 2 = 4” is a fact only if we accept certain ideas about what we mean by “2” and “+” and “=” and “4”. That we use those definitions instead of others is a reflection of what we find interesting or useful or attractive. There is cultural artifice behind the labelling of this equation as a fact.

Jimmy Johnson’s Arlo and Janis for the 18th capped off a week of trying to explain some point about the compression and dilution of time in comic strips. Comic strips use space and time to suggest more complete stories than they actually tell. They’re much like every other medium in this way. So, to symbolize deep thinking on a subject we get once again a panel full of mathematics. Yes, I noticed the misquoting of “E = mc²” there. I am not sure what Arlo means by “Remember the boat?” although thinking on it I think he did have a running daydream about living on a boat. Arlo and Janis isn’t a strongly story-driven comic strip, but Johnson is comfortable letting the setting evolve. Perhaps all this is forewarning that we’re going to jump ahead to a time in Arlo’s life when he has, or has had, a boat. I don’t know.

Terrible and Less-Terrible Pi

As the 14th of March comes around it’s the time for mathematics bloggers to put up whatever they can about π. I will stir from my traditional crankiness about Pi Day (look, we don’t write days of the year as 3.14 unless we’re doing fake stardates) to bring back my two most π-relevant posts:

• Calculating Pi Terribly is about a probability-based way to calculate just what π’s digits are. It’s a lousy way to do it, but it works, technically.
• Calculating Pi Less Terribly is about an analysis-based way to calculate just what π’s digits are. It’s a less bad way to do it, although we actually use better-yet ways to work out the digits of a number like this.
• And what the heck, Normal Numbers, from an A To Z sequence. We do not actually know that π is a normal number. It’s the way I would bet, though, and here’s something about why I’d bet that way.

Reading the Comics, January 14, 2017: Maybe The Last Jumble? Edition

So now let me get to the other half of last week’s comics. Also, not to spoil things, but this coming week is looking pretty busy so I may have anothe split-week Reading the Comics coming up. The shocking thing this time is that the Houston Chronicle has announced it’s discontinuing its comics page. I don’t know why; I suppose because they’re fed up with people coming loyally to a daily feature. I will try finding alternate sources for the things I had still been reading there, but don’t know if I’ll make it.

I’m saddened by this. Back in the 90s comics were just coming onto the Internet. The Houston Chronicle was one of a couple newspapers that knew what to do with them. It, and the Philadelphia Inquirer and the San Jose Mercury-News, had exactly what we wanted in comics: you could make a page up of all the strips you wanted to read, and read them on a single page. You could even go backwards day by day in case you missed some. The Philadelphia Inquirer was the only page that let you put the comics in the order you wanted, as opposed to alphabetical order by title. But if you were unafraid of opening up URLs you could reorder the Houston Chronicle page you built too.

And those have all faded away. In the interests of whatever interest is served by web site redesigns all these papers did away with their user-buildable comics pages. The Chronicle was the last holdout, but even they abolished their pages a few years ago, with a promise for a while that they’d have a replacement comics-page scheme up soon. It never came and now, I suppose, never will.

Most of the newspapers’ sites had become redundant anyway. Comics Kingdom and GoComics.com offer user-customizable comics pages, with a subscription model that makes it clear that money ought to be going to the cartoonists. I still had the Chronicle for a few holdouts, like Joe Martin’s strips or the Jumble feature. And from that inertia that attaches to long-running Internet associations.

So among the other things January 2017 takes away from us, it is taking the last, faded echo of the days in the 1990s when newspapers saw comics as awesome things that could be made part of their sites.

Lorie Ransom’s The Daily Drawing for the 11th is almost but not quite the anthropomorphized-numerals joke for this installment. It’s certainly the most numerical duck content I’ve got on record.

Tom II Wilson’s Ziggy for the 11th is an Early Pi Day joke. Cosmically there isn’t any reason we couldn’t use π in take-a-number dispensers, after all. Their purpose is to give us some certain order in which to do things. We could use any set of numbers which can be put in order. So the counting numbers work. So do the integers. And the real numbers. But practicality comes into it. Most people have probably heard that π is a bit bigger than 3 and a fair bit smaller than 4. But pity the two people who drew and figuring out who gets to go first. Still, I won’t be surprised if some mathematics-oriented place uses a gimmick like this, albeit with numbers that couldn’t be confused. At least not confused by people who go to mathematics-oriented places. That would be for fun rather than cake.

the Jumble for the 11th of January, 2017. This link’s all but sure to die the 1st of February, so, sorry about that. Mesopotamia did have the abacus, although I don’t know that the depiction is anything close to what the actual ones looked like. I’d imagine they do, at least within the limits of what will be an understandable drawing.

I can’t promise that the Jumble for the 11th is the last one I’ll ever feature here. I might find where David L Hoyt and Jeff Knurek keep a linkable reference to their strips and point to them. But just in case of the worst here’s an abacus gag for you to work on.

Corey Pandolph, Phil Frank, and Joe Troise’s The Elderberries for the 12th is, I have to point out, a rerun. So if you’re trying to do the puzzle the reference to “the number of the last president” isn’t what you’re thinking of. It is an example of the conflation of intelligence with skill at arithmetic. It’s also an example the conflation of intelligence with a mastery of trivia. But I think it leans on arithmetic more. I am not sure when this strip first appeared. “The last president” might have been Bill Clinton (42) or George W Bush (43). But this means we’re taking the square root of either 33 or 34. And there’s no doing that in your head. The square root of a whole number is either a whole number — the way the square root of 36 is — or else it’s an irrational number. You can work out the square root of a non-perfect-square by hand. But it’s boring and it’s worse than just writing “” or “”. Except in figuring out if that number is larger than or smaller than five or six. It’s good for that.

Dave Blazek’s Loose Parts for the 13th is the actuary joke for this installment. Actuarial studies are built on one of the great wonders of statistics: that it is possible to predict how often things will happen. They can happen to a population, as in forecasts of how many people will be in traffic accidents or fires or will lose their jobs or will move to a new city. We may have no idea to whom any of these will happen, and they may have no way of guessing, but the enormous number of people and great number of things that can combine to make a predictable state of affairs. I suppose it’s imaginable that a group could study its dynamics well enough to identify who screws up the most and most seriously. So they might be able to say what the odds are it is his fault. But I imagine in practice it’s too difficult to define screw-ups or to assign fault consistently enough to get the data needed.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 14th is another multiverse strip, echoing the Dinosaur Comics I featured here Sunday. I’ll echo my comments then. If there is a multiverse — again, there is not evidence for this — then there may be infinitely many versions of every book of the Bible. This suggests, but it does not mandate, that there should be every possible incarnation of the Bible. And a multiverse might be a spendthrift option anyway. Just allow for enough editions, and the chance that any of them will have a misprint at any word or phrase, and we can eventually get infinitely many versions of every book of the Bible. If we wait long enough.

Reading the Comics, September 6, 2016: Oh Thank Goodness We’re Back Edition

That’s a relief. After the previous week’s suspicious silence Comic Strip Master Command sent a healthy number of mathematically-themed comics my way. They cover a pretty normal spread of topics. So this makes for a nice normal sort of roundup.

Mac King and Bill King’s Magic In A Minute for the 4th is an arithmetic-magic-trick. Like most arithmetic-magic it depends on some true but, to me, dull bit of mathematics. In this case, that 81,234,567 minus 12,345,678 is equal to something. As a kid this sort of trick never impressed me because, well, anyone can do subtraction. I didn’t appreciate that the fun of stage magic in presenting well the mundane.

Jerry Scott and Jim Borgman’s Zits for the 5th is an ordinary mathematics-is-hard joke. But it’s elevated by the artwork, which shows off the expressive and slightly surreal style that makes the comic so reliable and popular. The formulas look fair enough, the sorts of things someone might’ve been cramming before class. If they’re a bit jumbled up, well, Pierce hasn’t been well.

Jerry Scott and Jim Borgman’s Zits for the 5th of September, 2016. It sure looks to me like there’s more things being explicitly multiplied by ‘1’ than are needed, but it might be the formulas got a little scrambled as Pierce vomited. We’ve all been there. Fun fact: apart from a bit in Calculus I where they drill you on differentiation formulas you never really need the secant. It makes a couple formulas a little more compact and that’s it, so if it’s been nagging at your mind go ahead and forget it.

Jeffrey Caulfield and Alexandre Rouillard’s Mustard and Boloney for the 6th is an anthropomorphic-shapes joke and I feel like it’s been here before. Ah, yeah, there it is, from about this time last year. It’s a fair one to rerun.

Mustard and Boloney popped back in on the 8th with a strip I don’t have in my archive at least. It’s your standard Pi Pun, though. If they’re smart they’ll rerun it in March. I like the coloring; it’s at least a pleasant panel to look at.

Percy Crosby’s Skippy from the 9th of July, 1929 was rerun the 6th of September. It seems like a simple kid-saying-silly-stuff strip: what is the difference between the phone numbers Clinton 2651 and Clinton 2741 when they add to the same number? (And if Central knows what the number is why do they waste Skippy’s time correcting him? And why, 87 years later, does the phone yell at me for not guessing correctly whether I need the area code for a local number and whether I need to dial 1 before that?) But then who cares what the digits in a telephone number add to? What could that tell us about anything?

As phone numbers historically developed, the sum can’t tell us anything at all. But if we had designed telephone numbers correctly we could have made it … not impossible to dial a wrong number, but at least made it harder. This insight comes to us from information theory, which, to be fair, we have because telephone companies spent decades trying to work out solutions to problems like people dialing numbers wrong or signals getting garbled in the transmission. We can allow for error detection by schemes as simple as passing along, besides the numbers, the sum of the numbers. This can allow for the detection of a single error: had Skippy called for number 2641 instead of 2741 the problem would be known. But it’s helpless against two errors, calling for 2541 instead of 2741. But we could detect a second error by calculating some second term based on the number we wanted, and sending that along too.

By adding some more information, other modified sums of the digits we want, we can even start correcting errors. We understand the logic of this intuitively. When we repeat a message twice after sending it, we are trusting that even if one copy of the message is garbled the recipient will take the version received twice as more likely what’s meant. We can design subtler schemes, ones that don’t require we repeat the number three times over. But that should convince you that we can do it.

The tradeoff is obvious. We have to say more digits of the number we want. It isn’t hard to reach the point we’re ending more error-detecting and error-correcting numbers than we are numbers we want. And what if we make a mistake in the error-correcting numbers? (If we used a smart enough scheme, we can work out the error was in the error-correcting number, and relax.) If it’s important that we get the message through, we shrug and accept this. If there’s no real harm done in getting the message wrong — if we can shrug off the problem of accidentally getting the wrong phone number — then we don’t worry about making a mistake.

And at this point we’re only a few days into the week. I have enough hundreds of words on the close of the week I’ll put off posting that a couple of days. It’s quite good having the comics back to normal.

Reading the Comics, July 2, 2016: Ripley’s Edition

As I said Sunday, there were more mathematics-mentioning comic strips than I expected last week. So do please read this little one and consider it an extra. The best stuff to talk about is from Ripley’s Believe It Or Not, which may or may not count as a comic strip. Depends how you view these things.

Randy Glasbergen’s Glasbergen Cartoons for the 29th just uses arithmetic as the sort of problem it’s easiest to hide in bed from. We’ve all been there. And the problem doesn’t really enter into the joke at all. It’s just easy to draw.

John Graziano’s Ripley’s Believe It Or Not on the 29th shows off a bit of real trivia: that 599 is the smallest number whose digits add up to 23. And yet it doesn’t say what the largest number is. That’s actually fair enough. There isn’t one. If you had a largest number whose digits add up to 23, you could get a bigger one by multiplying it by ten: 5990, for example. Or otherwise add a zero somewhere in the digits: 5099; or 50,909; or 50,909,000. If we ignore zeroes, though, there are finitely many different ways to write a number with digits that add up to 23. This is almost an example of a partition problem. Partitions are about how to break up a set of things into groups of one or more. But in a partition proper we don’t really care about the order: 5-9-9 is as good as 9-9-5. But we can see some minor differences between 599 and 995 as numbers. I imagine there must be a name for the sort of partition problem in which order matters, but I don’t know what it is. I’ll take nominations if someone’s heard of one.

Graziano’s Ripley’s sneaks back in here the next day, too, with a trivia almost as baffling as the proper credit for the strip. I don’t know what Graziano is getting at with the claim that Ancient Greeks didn’t consider “one” to be a number. None of the commenters have an idea either and my exhaustive minutes of researching haven’t worked it out.

But I wouldn’t blame the Ancient Greeks for finding something strange about 1. We find something strange about it too. Most notably, of all the counting numbers 1 falls outside the classifications of “prime” and “composite”. It fits into its own special category, “unity”. It divides into every whole number evenly; only it and zero do that, if you don’t consider zero to be a whole number. It’s the multiplicative identity, and it’s the numerator in the set of unit fractions — one-half and one-third and one-tenth and all that — the first fractions that people understand. There’s good reasons to find something exceptional about 1.

dro-mo for the 30th somehow missed both Pi Day and Tau Day. I imagine it’s a rerun that the artist wasn’t watching too closely.

Aaron McGruder’s The Boondocks rerun for the 2nd concludes that storyline I mentioned on Sunday about Riley not seeing the point of learning subtraction. It’s always the motivation problem.

Reading the Comics, June 29, 2016: Math Is Just This Hard Stuff, Right? Edition

We’ve got into that stretch of the year when (United States) schools are out of session. Comic Strip Master Command seems to have thus ordered everyone to clean out their mathematics gags, even if they didn’t have any particularly strong ones. There were enough the past week I’m breaking this collection into two segments, though. And the first segment, I admit, is mostly the same joke repeated.

Russell Myers’s Broom Hilda for the 27th is the type case for my “Math Is Just This Hard Stuff, Right?” name here. In fairness to Broom Hilda, mathematics is a lot harder now than it was 1,500 years ago. It’s fair not being able to keep up. There was a time that finding roots of third-degree polynomials was the stuff of experts. Today it’s within the powers of any Boring Algebra student, although she’ll have to look up the formula for it.

John McPherson’s Close To Home for the 27th is a bunch of trigonometry-cheat tattoos. I’m sure some folks have gotten mathematics tattoos that include … probably not these formulas. They’re not beautiful enough. Maybe some diagrams of triangles and the like, though. The proof of the Pythagoran Theorem in Euclid’s Elements, for example, includes this intricate figure I would expect captures imaginations and could be appreciated as a beautiful drawing.

Missy Meyer’s Holiday Doodles observed that the 28th was “Tau Day”, which takes everything I find dubious about “Pi Day” and matches it to the silly idea that we would somehow make life better by replacing π with a symbol for 2π.

Hilary Price’s Rhymes With Orange for the 29th of June, 2016. I like the Number-two-pencil fence.

Hilary Price’s Rhymes With Orange for the 29th uses mathematics as the way to sort out nerds. I can’t say that’s necessarily wrong. It’s interesting to me that geometry and algebra communicate “nerdy” in a shorthand way that, say, an obsession with poetry or history or other interests wouldn’t. It wouldn’t fit the needs of this particular strip, but I imagine that a well-diagrammed sentence would be as good as a page full of equations for expressing nerdiness. The title card’s promise of doing quadratic equations would have worked on me as a kid, but I thought they sounded neat and exotic and something to discover because they sounded hard. When I took Boring High School Algebra that charm wore off.

Aaron McGruder’s The Boondocks rerun for the 29th starts a sequence of Riley doubting the use of parts of mathematics. The parts about making numbers smaller. It’s a better-than-normal treatment of the problem of getting a student motivated. The strip originally ran the 18th of April, 2001, and the story continued the several days after that.

Bill Whitehead’s Free Range for the 29th uses Boring Algebra as an example of the stuff kinds have to do for homework.

Reading the Comics, April 15, 2016: Remarkably, No Income Tax Comics Edition

I’m as startled as you are. While a couple comic strips mentioned United States Income Tax Day, they didn’t do so in a way that seemed on-point enough for this Reading The Comics post. Of course, United States Income Tax Day happens to be the 18th this year. I haven’t seen Sunday’s comics yet.

David L Hoyt and Jeff Knurek’s Jumble for the 11th of April one again uses arithmetic puns for its business. Also, if some science fiction writer doesn’t take hold of “Gribth” as a name for something they’re missing a fine syllable. “Tahew” is no slouch in the made-up word leagues either.

David L Hoyt and Jeff Knurek’s Jumble for the 11th of April, 2016. The link will probably expire sometime before the year 2112.

Ryan North’s Dinosaur Comics for the 12th of April obviously originally ran sometime in mid-March. I have similarly ambiguous feelings about the value of Pi Day. I suppose it’s nice for people to think of “fun” and “mathematics” close together. Utahraptor’s distinction between “Pi Day” of March 14 and “Approximate Pi Day” of the 22nd of July s a curious one, though. It’s not as though 3.14 is any more exactly π than 22/7 is. I suppose you can argue that at some moment on 3/14 between 1:59:26 and 1:59:27 there’s some moment, 1:59:26.5358979 et cetera going on forever. But that assumes that time is a continuous thing, and it’s not like you’ll ever know what that moment is. By the time you might recognize it, it’s passed. They are all Approximate Pi Days; we just have to decide what the approximation is.

Bill Schorr’s The Grizzwells for the 12th is a silly-homework problem question. I know the point is to joke about how Fauna misunderstands a word. But if we pretend the assignment is for real, what might its point be? To show that students know the parts of a right triangle? I guess that’s all right, but it doesn’t seem like much of an assignment. I don’t blame her for getting snarky in the face of that.

Rick Kirkman and Jerry Scott’s Baby Blues for the 13th is a gag about picking random numbers for arithmetic homework. The approach is doomed, surely, although it’s probably not completely doomed. I’m not sure Hammie’s age, but if his homework is about adding and subtracting numbers he probably mostly gets problems that give results between zero and twenty, and almost always less than a hundred. He might hit some by luck.

Rick Kirkman and Jerry Scott’s Baby Blues for the 13th of April, 2016. It’s only after Hammy walks away that Zoe wonders why he needs five random numbers?

I’ve mentioned some how people are awful at picking “random” numbers in their heads. Zoe shows off one of the ways people are bad at it. People asked to name numbers “randomly” pick odd numbers more than even numbers. Somehow they just feel random. I doubt Kirkman and Scott were thinking of that; among other things, five numbers is a very small sample. Four odds out of five isn’t peculiar, not yet. They were probably just trying to pick numbers that sounded funny while fitting the space available. I’m a bit surprised 37 didn’t make the list.

Mark Anderson’s Andertoons for the 13th is Mark Anderson’s Andertoons entry for this essay. I like the teacher’s answer, though.

Patrick Roberts’s Todd the Dinosaur for the 14th just uses arithmetic as the most economic way to fit several problems on-screen at once. They’ve got a compactness that sentence-diagramming just can’t match.

Patrick Roberts’s Todd the Dinosaur for the 14th of April, 2016. No fair wondering why his more distant eye is always the larger one.

Greg Cravens’s The Buckets for the 15th amuses me with its use of coin-tossing as a way of making choices. I’m also amused the coin might be wrong only about half the time.

John Deering’s Strange Brew for the 15th is a visual puzzle. It’s intending to make use of a board full of mathematical symbols to represent deep thought. But the symbols aren’t quite mathematics. They look much more like LaTeX, a typesetting code used to express mathematics in print. Some of the symbols are obscured, so I can’t say exactly what’s meant. But it should be something like this:

At the risk of disappointing, this appears to me gibberish. The appearance of words like ‘minPixels’ and ‘maxPixels’ suggest a bit of computer code. So does having a subscript that’s the full word “connected”. I wonder where Deering drew this example from.

Reading the Comics, March 14, 2016: Pi Day Comics Event

Comic Strip Master Command had the regular pace of mathematically-themed comic strips the last few days. But it remembered what the 14th would be. You’ll see that when we get there.

Ray Billingsley’s Curtis for the 11th of March is a student-resists-the-word-problem joke. But it’s a more interesting word problem than usual. It’s your classic problem of two trains meeting, but rather than ask when they’ll meet it asks where. It’s just an extra little step once the time of meeting is made, but that’s all right by me. Anything to freshen the scenario up.

Ray Billingsley’s Curtis for the 11th of March, 2016. I am curious what the path of the rail line is.

Tony Carrillo’s F Minus for the 11th was apparently our Venn Diagram joke for the week. I’m amused.

Mason Mastroianni, Mick Mastroianni, and Perri Hart’s B.C. for the 12th of March name-drops statisticians. Statisticians are almost expected to produce interesting pictures of their results. It is the field that gave us bar charts, pie charts, scatter plots, and many more. Statistics is, in part, about understanding a complicated set of data with a few numbers. It’s also about turning those numbers into recognizable pictures, all in the hope of finding meaning in a confusing world (ours).

Brian Anderson’s Dog Eat Doug for the 13th of March uses walls full of mathematical scrawl as signifier for “stuff thought deeply about’. I don’t recognize any of the symbols specifically, although some of them look plausibly like calculus. I would not be surprised if Anderson had copied equations from a book on string theory. I’d do it to tell this joke.

And then came the 14th of March. That gave us a bounty of Pi Day comics. Among them:

John Hambrock’s The Brilliant Mind of Edison Lee for the 14th of March, 2016. The strip is like this a lot.

John Hambrock’s The Brilliant Mind of Edison Lee trusts that the name of the day is wordplay enough.

Scott Hilburn’s The Argyle Sweater is also a wordplay joke, although it’s a bit more advanced.

Tim Rickard’s Brewster Rockit fuses the pun with one of its running, or at least rolling, gags.

Bill Whitehead’s Free Range makes an urban legend out of the obsessive calculation of digits of π.

And Missy Meyer’s informational panel cartoon Holiday Doodles mentions that besides “National” Pi Day it was also “National” Potato Chip Day, “National” Children’s Craft Day, and “International” Ask A Question Day. My question: for the first three days, which nation?

Edited To Add: And I forgot to mention, after noting to myself that I ought to mention it. The Price Is Right (the United States edition) hopped onto the Pi Day fuss. It used the day as a thematic link for its Showcase prize packages, noting how you could work out π from the circumference of your new bicycles, or how π was a letter from your vacation destination of Greece, and if you think there weren’t brand-new cars in both Showcases you don’t know the game show well. Did anyone learn anything mathematical from this? I am skeptical. Do people come away thinking mathematics is more fun after this? … Conceivably. At least it was a day fairly free of people declaring they Hate Math and Can Never Do It.