• #### Joseph Nebus 3:13 pm on Wednesday, 20 May, 2015 Permalink | Reply Tags: adding machines, amusements, beach, games ( 2 ), Gottleib, pinball ( 3 ), secretaries

Last weekend I visited the Vintage Flipper World pinball museum just outside Ann Arbor, Michigan. Among the games there was Gottleib’s 1955 table Sweet Add-A-Line. It’s a peculiar table by modern standards, since nearly all the playfield is a bunch of lanes, channels through which the pinball might roll. But …

In this round of Sweet Add-A-Line I managed to get the 9, 7, 15, and 2 rollovers, lighting up the total of 33 on the lower-left adding tape. And scored overall 1,840,000 points. See the lights at the bottom. Unanswered question: so, “patio secretary” was a thing in 1955? I guess?

I apologize for the Coors sign reflected in the back glass. I didn’t even see it when I was taking the picture.

Each of the lanes is numbered. Rolling one down lights up that number in the backglass, as above. And if you roll all the numbers in one of the eight strips of tape, the game opens up bonus opportunities. It’s a fun game and certainly one of the top adding-machine-themed pinball machines I’ve ever played. I grant this is of marginal mathematical content, but, heck, I smiled.

The Internet Pinball Database has a scan of the game’s advertising flyer, which I like if nothing else for its defensive “Amusement Pinballs: as American as Baseball and Hot Dogs!” slogan.

• #### baffledbaboon 3:19 pm on Wednesday, 20 May, 2015 Permalink | Reply

A pinball museum? Sounds like heaven. In every arcade I have ever been to, I always find myself drifting towards the pinball machines.

• #### Joseph Nebus 5:34 pm on Wednesday, 20 May, 2015 Permalink | Reply

It is indeed a great place. Unfortunately it’s only rarely open to the public (zoning problems). But there are wonderful and generally-open museums for pinball. The most famous is in Las Vegas — that one’s credited with leading the current happy revival of pinball — although the one I know best is the Silverball Museum in Asbury Park, New Jersey. Well worth getting to if you’re in the Garden State.

• #### baffledbaboon 5:46 pm on Wednesday, 20 May, 2015 Permalink | Reply

Thanks so much! I am definitely adding this to my list of places to go.

• #### Joseph Nebus 4:24 am on Friday, 22 May, 2015 Permalink | Reply

It’s certainly worth it. Well, the ones I’ve been to are. There are a couple arcades with a healthy number of pinball machines too. I’m happy to say Michigan is one of the centers of the current pinball renaissance.

• #### sheldonk2014 2:56 am on Thursday, 21 May, 2015 Permalink | Reply

There’s nothing like a pinball machine,one wrong move and it titles,it doesn’t get any better then that

• #### Joseph Nebus 4:27 am on Friday, 22 May, 2015 Permalink | Reply

No, there isn’t anything like that. The appeal of real things that move is a powerful one. Well, and making the right move where you slide the machine, save the ball, and get away with it. That’s really powerful.

• #### Oscar Hills 12:17 pm on Thursday, 21 May, 2015 Permalink | Reply

I own one of these and love it. I got a Google alert on your post because I’m always on the lookout for a better specimen of SAAL. What makes it such a great game is the massive adrenaline rush of the “replay” that existed at the height of these games in the ’50’s combined with the unique fact that in SAAL if you roll over all the lanes, you score 26 replays – you max out the replay reel. That’s was a rush beyond compare “back in the day.”

• #### Joseph Nebus 6:34 am on Friday, 22 May, 2015 Permalink | Reply

I’m glad to hear from someone who owns one! I wasn’t able to get more than one column of numbers completed in the limited time I had to play. (The museum is unfortunately open to the public only a few times a year, but it’s got a great selection of 1950s machines to play.) Just the thought of maxing out the replay reel is awesome, though. If I ever do it … well, wow.

## Calculating Pi Less Terribly

Back on “Pi Day” I shared a terrible way of calculating the digits of π. It’s neat in principle, yes. Drop a needle randomly on a uniformly lined surface. Keep track of how often the needle crosses over a line. From this you can work out the numerical value of π. But it’s a terrible method. To be sure that π is about 3.14, rather than 3.12 or 3.38, you can expect to need to do over three and a third million needle-drops. So I described this as a terrible way to calculate π.

A friend on Twitter asked if it was worse than adding up 4 * (1 – 1/3 + 1/5 – 1/7 + … ). It’s a good question. The answer is yes, it’s far worse than that. But I want to talk about working π out that way.

Tom Batiuk’s Funky Winkerbean for the 17th of May, 2015. The worst part of this strip is Science Teacher Mark Twain will go back to the teachers’ lounge and complain that none of his students got it.

This isn’t part of the main post. But the comic strip happened to mention π on a day when I’m talking about π so who am I to resist coincidence?

(More …)

• #### Matthew Wright 9:30 pm on Sunday, 17 May, 2015 Permalink | Reply

I tried memorising pi once, but for some reason I couldn’t finish. It wasn’t very rational of me. I sort of had to say that. (Actually, I probably didn’t…)

• #### Joseph Nebus 5:27 pm on Wednesday, 20 May, 2015 Permalink | Reply

Aw, not to fear. I don’t think worse of you for saying it. It is the kind of joke people have to say, after all.

• #### abyssbrain 3:40 am on Monday, 18 May, 2015 Permalink | Reply

It’s really difficult to manually calculate pi using a series. William Shanks claimed to have calculated pi manually up to more than 700 digits using the Machin’s formula,

$\frac{\pi}{4}=4\arctan \frac{1}{5}-\arctan \frac{1}{239}$

but he erred on the 528th digit, I think. It was a very amazing achievement nonetheless.

• #### Joseph Nebus 5:31 pm on Wednesday, 20 May, 2015 Permalink | Reply

Shanks’s case is interesting, not just because of his great work and tragic error. There is also that museum rotunda that tries to honor him by displaying the digits of pi; it was built before his error was found.

So the question is: keep the digits he calculated which are wrong, or replace them with the digits he would have calculated had he done the work right? Bearing in mind the purpose is to honor Shanks’s work, and nobody is going to get the digits of pi from reading what is essentially a piece of memorial art.

## Reading the Comics, May 14, 2015: At The Cash Register Edition

This might not be the most exciting week of mathematically-themed comic strips. But it gives me the chance to be more autobiographical than usual. And it’s got more reruns than average, too.

Also, I’m trying out a new WordPress Theme. I’m a little suspicious of it myself, but will see what I think of it a week from now. Don’t worry, I remember the name of the old one in case I want to go back. Also, WordPress Master Command: stop hiding the option to live-preview themes instead of switching to them right away.

Norm Feuti’s Retail For the 11th of May, 2015.

Norm Feuti’s Retail (May 11) led off a week of “Epic Customer Fails” with an arithmetic problem. My own work in retail was so long ago and for so short a time I don’t remember this happening. But I can believe in a customer being confused this way. I think there is a tendency to teach arithmetic problems as a matter of “pick out the numbers, pick out the operation, compute that”. This puts an emphasis placed on computing quickly. That seems to invite too-quick calculation of not-quite the right things. That percentages are a faintly exotic construct to many people doesn’t help either.

My own retail customers-with-percentages story is duller. A customer asked about a book, I believe an SAT preparation book, which had a 20 percent (or whatever) off sticker. He specifically wanted to know whether 20 percent was taken off the price before the sales tax (6 percent) was calculated, or whether the registers added the sales tax and then took 20 percent off that total. I tried to reassure him that it didn’t matter, the resulting price would be the same. He tried to reassure me that it did matter because the sales tax should be calculated on the price paid, not reduced afterward. I believed, then and now, that he was right legally, but for the practical point of how much he had to pay it made no difference.

He judged me warily, but I worked out what the price paid would be, and he let me ring the book up. And the price came out about a dollar too high. The bar code had a higher price for the book than the plain-english corner said. He snorted “Ha!” and may have told me so. I explained the problem, showing the bar code version of the price (it’s in the upper-right corner of the bar code on books) and the price I’d used to calculate. He repeated that this was why he had asked, while I removed the wrong price and entered the thing manually so I could put in the lower price. And took the 20 percent off, and added sales tax, which came out to what I had said the price was.

I don’t believe I ever saw him again, but I would like the world to know that I was right. And the SAT prep book-maker needed to not screw up their bar codes.

• #### sheldonk2014 4:21 pm on Friday, 15 May, 2015 Permalink | Reply

Are you saying there is a mathematical theory to how and why we die or even when it where,I guess if you step back and I think for a second I can see this understanding
Sheldonn

• #### Joseph Nebus 6:07 pm on Friday, 15 May, 2015 Permalink | Reply

Well, what do you mean by a theory? Since governments started raising money by selling annuities they’ve studied how long people are likely to live, and how many are likely to die — and from what causes — in any given area in a given year. That’s in some sense a theory of how and when people do die. And demographers study how people move about, and what for; that would look at where and why.

That’s whole populations, though. And it’s the somewhat strange idea that we could say pretty reliably that (say) 300 people in this area will die over the coming year, but have no idea of which ones, or just when in the year they would. We can use that for individual predictions, though: if you’re a person of this age range, and have this set of medical conditions, and so on, then we can find a group of people you’re generally like and suppose you’ll live about as long as typical for that group.

On an individual body experience, studying the mathematics of how bodies work — how nutrients and oxygen are spread out, how the body’s cells reproduce and decay and even die, how they thrive and how they break down — is a lot of good work to be done too. In graduate school I even did a course on medical mathematics, although that studied more very specific topics like how to infer how nerve pulses flow around the heart from the signals provided by an electrocardiogram. That is a theory about how bodies work, and why, although that might not be quite what you’re thinking of.

• #### ivasallay 12:36 pm on Saturday, 16 May, 2015 Permalink | Reply

I always enjoy Retail, and you made it even better with your story about selling the SAT prep book!

• #### Joseph Nebus 5:08 pm on Sunday, 17 May, 2015 Permalink | Reply

Aw, thanks. I’m glad you liked.

• #### sheldonk2014 4:28 am on Monday, 18 May, 2015 Permalink | Reply

I am a two dimensiona person living in a three dimensional world

• #### Joseph Nebus 5:31 pm on Wednesday, 20 May, 2015 Permalink | Reply

Ah, but if you play your cards right, you could still fill a volume.

## Reversible and irreversible change

Entropy is hard to understand. It’s deceptively easy to describe, and the concept is popular, but to understand it is challenging. In this month’s entry CarnotCycle talks about thermodynamic entropy and where it comes from. I don’t promise you will understand it after this essay, but you will be closer to understanding it.

Originally posted on carnotcycle:

Reversible change is a key concept in classical thermodynamics. It is important to understand what is meant by the term as it is closely allied to other important concepts such as equilibrium and entropy. But reversible change is not an easy idea to grasp – it helps to be able to visualize it.

Reversibility and mechanical systems

The simple mechanical system pictured above provides a useful starting point. The aim of the experiment is to see how much weight can be lifted by the fixed weight M1. Experience tells us that if a small weight M2 is attached – as shown on the left – then M1 will fall fast while M2 is pulled upwards at the same speed.

Experience also tells us that as the weight of M2 is increased, the lifting speed will decrease until a limit is reached when the weight difference between M2 and M1 becomes…

View original 692 more words

• #### sheldonk2014 9:51 pm on Tuesday, 12 May, 2015 Permalink | Reply

The only dynamics I want to experience is how much strength does it take to lift my but or the kinetics it takes it takes to lift my arm to my noise
As always Sheldon

• #### Joseph Nebus 4:11 pm on Friday, 15 May, 2015 Permalink | Reply

Ah, but even those dynamics are amazing. And the way the body works can tell us amazing things about the way physics works: Julius von Mayer’s observations that people’s blood was a deeper red — holding more oxygen — in the tropics compared to in Europe was one of the pieces leading people to the conservation of energy. Hermann von Helmholtz’s career in physics was inspired, in part, by a teacher proclaiming no one would ever know how fast a nerve impulse travelled; and he didn’t believe it, and became one of science’s immortals. There’s astounding things like this everywhere.

## Reading the Comics, May 9, 2015: Trapezoid Edition

And now I get caught up again, if briefly, to the mathematically-themed comic strips I can find. I’ve dubbed this one the trapezoid edition because one happens to mention the post that will outlive me.

Todd Clark’s Lola (May 4) is a straightforward joke. Monty’s given his chance of passing mathematics and doesn’t understand the prospect is grim.

Joe Martin’s Willy and Ethel for the 4th of May, 2015. The link will likely expire in early June.

Joe Martin’s Willy and Ethel (May 4) shows an astounding feat of mind-reading, or of luck. How amazing it is to draw a number at random from a range depends on many things. It’s less impressive to pick the right number if there are only three possible answers than it is to pick the right number out of ten million possibilities. When we ask someone to pick a number we usually mean a range of the counting numbers. My experience suggests it’s “one to ten” unless some other range is specified. But the other thing affecting how amazing it is is the distribution. There might be ten million possible responses, but if only a few of them are likely then the feat is much less impressive.

The distribution of a random number is the interesting thing about it. The number has some value, yes, and we may not know what it is, but we know how likely it is to be any of the possible values. And good mathematics can be done knowing the distribution of a value of something. The whole field of statistical mechanics is an example of that. James Clerk Maxwell, famous for the equations which describe electromagnetism, used such random variables to explain how the rings of Saturn could exist. It isn’t easy to start solving problems with distributions instead of particular values — I’m not sure I’ve seen a good introduction, and I’d be glad to pass one on if someone can suggest it — but the power it offers is amazing.

• #### sheldonk2014 10:32 pm on Saturday, 9 May, 2015 Permalink | Reply

I love the Stan Drake strip
As always Sheldon

• #### Joseph Nebus 3:36 am on Monday, 11 May, 2015 Permalink | Reply

Glad you like it. I’ve been intrigued by The Heart of Juliet Jones as a great example of the romance/soap-opera strip and for being occasionally very funny in how it hews to the genre conventions.

• #### ivasallay 1:11 am on Sunday, 10 May, 2015 Permalink | Reply

Thanks for introducing me to that classic strip Skippy.

• #### Joseph Nebus 3:37 am on Monday, 11 May, 2015 Permalink | Reply

Happy to. It’s one of the underrated gems of 20th century American comics.

• #### elkement 7:51 am on Tuesday, 12 May, 2015 Permalink | Reply

Yes, the E=mc2 joke hurts a bit – thinking about units ;-)

• #### Joseph Nebus 4:05 pm on Friday, 15 May, 2015 Permalink | Reply

Aw, all unit problems can be worked out by just not paying attention to them.

• #### chattykerry 9:31 pm on Tuesday, 12 May, 2015 Permalink | Reply

I feel like Penny in the Big Bang Theory when reading your site… Clearly, only the left side of my brain works. :) Thank you for enjoying my guest blog on Jumbled Writer.

• #### Joseph Nebus 4:07 pm on Friday, 15 May, 2015 Permalink | Reply

Aw, goodness, don’t be hard on yourself. Everyone can do mathematics and ought to feel like they’re welcome to.

I promise: if something I write seems unclear, tell me. I’ll do my best to be more understandable.

## Reading the Comics, May 4, 2015: Hatless Aliens Edition

I have to make two confessions for this round of mathematics comic strips. First is that I was busy for like two days and missed about a jillion comic strips. So this is the first part of some catching-up to do. The second is that I don’t have a favorite of this bunch. The most interesting, I suppose, is the Mr Boffo, because it lets me get into a little trivia about Albert Einstein. But there’s not any in this bunch that made me smile much or that gave me a juicy topic to discuss. Maybe tomorrow.

Steve Breen and Mike Thompson’s Grand Avenue ran a week of snarky-answers-to-word-problems strips. April 28th, April 30th, and May 2nd featured mathematics questions. This must reflect how easy it is to undermine the logic of a mathematics question. The April 27th strip is about using Roman numerals, which I suppose is arithmetic. I’m not sure there’s much point to learning Roman numerals. We don’t do any calculations using the Roman numeral scheme except to show why Arabic numerals are better. All you get from Roman numerals is an ability to read building cornerstones and movie copyright dates. At least learning cursive handwriting provides the learner with a way to make illegible notes.

• #### ivasallay 4:37 pm on Saturday, 9 May, 2015 Permalink | Reply

I got a soft chuckle from that Roman numeral comic.

• #### Joseph Nebus 3:25 am on Monday, 11 May, 2015 Permalink | Reply

It is a good, reliable joke form, of the “Say goodnight, Gracie” structure.

• #### Matthew Wright 11:54 am on Monday, 11 May, 2015 Permalink | Reply

I’ve heard various stories about where Einstein got the inspiration for Special Relativity from (apart from extending Hendrik Lorentz) – including sitting on trams watching other trams run by, and/or thinking about how elements of gramophone records related to each other during dull times in the patent office. All of them are probably apocryphal.

• #### Joseph Nebus 4:05 pm on Friday, 15 May, 2015 Permalink | Reply

I believe that Einstein had described how he stared at trains, and at the train station’s clock — which had several faces for the different train lines, from the days before standard time zone — as something he did. I’m not sure how much this inspired thinking about what it meant to say “this is the time”, or “these two events are simultaneous”. It may have just been that it was a soothing, pleasantly orderly thing to look at. I’m unfortunately far from the references I faintly remember describing the scene better, though.

## What Do I Need To Pass This Class? (December 2014 Edition)

I don’t mean to repeat myself too much, but it is finals season for United States colleges on a semesterly schedule so, here. Good luck, people who’re minutes away from their final exams.

Originally posted on nebusresearch:

It’s finals season, at least for colleges that run on a semesterly schedule, and a couple of my posts are turning up in search query results again. So I thought it worth drawing a little more attention to them and hopefully getting people what they need sooner.

The answer: you need to study a steady but not excessive bit every night from now to before the exam; you need to get a full night of sleep before the exam; and you really needed to pay attention in class and do the fiddly little assignments all semester, so, sorry it’s too late for that. Also you need to not pointlessly antagonize your professor; even if you don’t like this class, you could have taken others to meet your academic requirement, so don’t act like you were dragged into Topics in Civilization: Death against your will even if it does satisfy three

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## How April 2015 Treated My Mathematics Blog

(I apologize if the formatting is messed up. For some reason preview is not working, and I will not be trying the new page for entering posts if I can at all help it. I will fix when I can, if it needs fixing.)

As it’s the start of the month I want to try understanding the readership of my blogs, as WordPress gives me statistics. It’s been a more confusing month than usual, though. One thing is easy to say: the number of pages read was 1,047, an all-time high around these parts for a single month. It’s up from 1,022 in March, and 859 in February. And it’s the second month in a row there’ve been more than a thousand readers. That part’s easy.

The number of visitors has dropped. It was down to 389 in April, from a record 468 in March and still-higher 407 in April. This is, if WordPress doesn’t lead me awry, my fifth-highest number of viewers. This does mean the number of views per visitor was my highest since June of 2013. The blog had 2.69 views per visitor, compared to 2.18 in March and 2.11 in February. It’s one of my highest views-per-visitor on record anyway. Perhaps people quite like what they see and are archive-binging. I approve of this. I’m curious why the number of readers dropped so, though, particularly when I look at my humor blog statistics (to be posted later).

I’m confident the readers are there, though. The number of likes on my mathematics blog was 297, up from March’s 265 and February’s 179. It’s the highest on record far as WordPress will tell me. So readers are more engaged, or else they’re clicking like from the WordPress Reader or an RSS feed. Neither gets counted as a page view or a visitor. That’s another easy part. The number of comments is down to 64, from March’s record 93, but March seems to have been an exceptional month. February had 56 comments so I’m not particularly baffled by April’s drop.

May starts out with 23,884 total views, and 472 people following specifically through WordPress.

It’s a truism that my most popular posts are the trapezoids one and the Reading The Comics posts, but for April that was incredibly true. Most popular the past thirty days were:

I am relieved that I started giving all these Comics posts their own individual “Edition” titles. Otherwise there’d be no way to tell them apart.

The nations sending me the most readers were, as ever, the United States (662), Canada (82), and the United Kingdom (47), with Slovenia once again strikingly high (36). Hong Kong came in with 24 readers, Italy 23, and Austria a mere 18. Elke Stangl’s had a busy month, I know.

This month’s single-reader countries were Czech Republic, Morocco, the Netherlands, Puerto Rico, Romania, Taiwan, and Vietnam. Romania’s the only one that sent me a single reader last month. India bounced back from five readers to six.

Among the search terms bringing people to me were no poems. Among the interesting phrases were:

• what point is driving the area difference between two triangles (A good question!)
• how do you say 1,898,600,000,000,000,000,000,000,000 (I almost never do.)
• is julie larson still drawing the dinette set (Yes, to the best of my knowledge.)
• jpe fast is earth spinning? (About once per day, although the answer can be surprisingly difficult to say! But also figure about 465 times the cosine of your latitude meters per second, roughly.)
• origin is the gateway to your entire gaming universe. (Again, I don’t know what this means, and I’m a little scared to find out.)
• i hate maths 2015 photos (Well, that just hurts.)
• getting old teacher jokes (Again, that hurts, even if it’s not near my birthday.)
• two trapezoids make a (This could be a poem, actually.)
• how to draw 2 trapezoids (I’d never thought about that one. Shall have to consider writing it.)

I don’t know quite what it all means, other than that I need to write about comic strips and trapezoids more somehow.

• #### scifihammy 4:34 pm on Friday, 1 May, 2015 Permalink | Reply

While I think it is great fun looking at all the stats – and who doesn’t? – I still think the main point is to enjoy blogging. If you enjoy it, chances are your readers will :)
As for trying to make sense if the numbers, if you ever do – let me know!! :)

• #### Joseph Nebus 6:08 am on Tuesday, 5 May, 2015 Permalink | Reply

Oh, certainly, the important thing is enjoying the blogging. And mostly I do enjoy the writing. Sometimes I end up afraid of the comments, but I try to overcome that.

• #### scifihammy 1:05 pm on Tuesday, 5 May, 2015 Permalink | Reply

Aw – mostly the WP people write nice stuff :) Though sometimes I don’t understand their comments! :)

• #### Joseph Nebus 9:46 pm on Wednesday, 6 May, 2015 Permalink | Reply

You’ve noticed that too? The comments seem nice enough but werble flazeeem galordle oompta imney?

• #### scifihammy 3:26 am on Thursday, 7 May, 2015 Permalink | Reply

hahaha :)

• #### Angie Mc 7:15 pm on Friday, 1 May, 2015 Permalink | Reply

OK, Joseph, I’m inching ever closer to doing something with my stats! I’m at least looking at them now :D One thing I like about them is the personal challenge of trying to work hard to engage with others. Looking at the bar graph go up and down helps to keep me motivated in its own way. Congrats on your all time high page reads!

• #### Joseph Nebus 6:09 am on Tuesday, 5 May, 2015 Permalink | Reply

I love looking at the statistics that say how much more a particular essay is read one week compared to the week before. I’m not so fond of the statistics that say how much less a particular essay is read one week compared to the week before. But I don’t know how to get the first without the second. Yet.

• #### Angie Mc 2:04 pm on Tuesday, 5 May, 2015 Permalink | Reply

Oooo, you figure that out, Joseph, and I’m all ears.

• #### Joseph Nebus 9:46 pm on Wednesday, 6 May, 2015 Permalink | Reply

Listing countries. It’s the only thing I know works for sure.

• #### Ken Dowell 9:01 pm on Friday, 1 May, 2015 Permalink | Reply

The WordPress stats are all very fascinating but I sometimes think they raise more questions than they answer.

• #### Joseph Nebus 6:12 am on Tuesday, 5 May, 2015 Permalink | Reply

Oh, do they ever. Mostly “counting trapezoids? That’s all people want of me?” Sometimes I fear I know what a one-hit wonder’s life is like.

• #### elkement 7:31 pm on Saturday, 2 May, 2015 Permalink | Reply

Only 18?? ;-) I would have guessed something more like 30-40? I wonder if one of my AdBlocker thingies on one of my computers prevents WP Stats from collecting my clicks?

• #### Joseph Nebus 6:27 am on Tuesday, 5 May, 2015 Permalink | Reply

Only 18, so it says. But I have wondered if something is blocking reads from showing up in WordPress statistics. I had a weird blip in my humor blog’s readership in April and I’m still not sure what (if anything) accounts for it.

## Earth Day

It’s a lovely day, so I felt like sharing these illustrations from the Life Through A Mathematicians Eyes blog. It’s simply superimposing graphs of equations over scenes of natural beauty, but that’s attractive enough.

When I say “graphs of equations”, I mean that we’re setting a coordinate system — here a Cartesian or rectangular one, one based on x- and y- and z- distances from some origin point — over space, and then drawing in white lines the sets of x- and y- and z-coordinates which make some equation true. That’s what we normally mean by saying “the graph of an equation”; it’s a drawing that shows when a relationship is true and when it is not.

Originally posted on Life Through A Mathematician's Eyes:

I believe most of you know what Earth Day is celebrating ^_^ I think this is a great day and there are a lot of activities that could be done everywhere to celebrate it. You might think that there is not much I can say about Earth and mathematics, but if you are a math – lover like you already know a lot of mathematical shapes, patterns and constant that can be found in nature. If you want to see more about this check the photos from my album Math&Nature .

But today I want to talk a little about the idea of an American student, mathematician and photographer, Nikki Graziano. I believe the project is old, but still very interesting and perfect for today. She took photos of different natural forms and then found proper equations to explain those forms created by nature. Here are some of the images:

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• #### ioanaiuliana 4:58 pm on Thursday, 30 April, 2015 Permalink | Reply

Thank you very much for sharing this :) Hope you had a fun Earth Day ^_^

• #### Joseph Nebus 6:04 am on Tuesday, 5 May, 2015 Permalink | Reply

Thank you. I’m happy to say I did, too.

• #### n2sz 11:48 am on Saturday, 2 May, 2015 Permalink | Reply

That plant looks suspiciously like some invasive species, which is what most of my students think math is in their brain….

• #### Joseph Nebus 6:25 am on Tuesday, 5 May, 2015 Permalink | Reply

Could be. Might be worth it finding some percolation problems to use, if any students would believe they used to make coffee by percolation, anyway.

## Reading the Comics, April 27, 2015: Anthropomorphic Mathematics Edition

They’re not running at the frantic pace of April 21st, but there’s still been a fair clip of comic strips that mention some kind of mathematical topic. I imagine Comic Strip Master Command wants to be sure to use as many of these jokes up as possible before the (United States) summer vacation sets in.

Dan Thompson’s Brevity (April 23) is a straightforward pun strip. It also shows a correct understanding of how to draw a proper Venn Diagram. And after all why shouldn’t an anthropomorphized Venn Diagram star in movies too?

John Atkinson’sWrong Hands (April 23) gets into more comfortable territory with plain old numbers being anthropomorphized. The 1 is fair to call this a problem. What kind of problem depends on whether you read the x as a multiplication sign or as a variable x. If it’s a multiplication sign then I can’t think of any true statement that can be made from that bundle of symbols. If it’s the variable x then there are surprisingly many problems which could be made, particularly if you’re willing to count something like “x = 718” as a problem. I think that it works out to 24 problems but would accept contrary views. This one ended up being the most interesting to me once I started working out how many problems you could make with just those symbols. There’s a fun question for your combinatorics exam in that.

• #### sheldonk2014 10:12 pm on Monday, 27 April, 2015 Permalink | Reply

I tried to give props to all my comic people on the weekend by writing a poem about the movie Pink Flamingos no one got it, it’s called Eddy,please tell me you have heard of this movie,otherwise I will crawl back in the corner and suck my dust

• #### Joseph Nebus 2:48 am on Wednesday, 29 April, 2015 Permalink | Reply

I’m honestly surprised. I would have thought that even if one hadn’t seen Pink Flamingos at least the title would be familiar as a movie. Possibly it’s a generational thing.

• #### abyssbrain 2:05 am on Tuesday, 28 April, 2015 Permalink | Reply

Yes, I agree. Quickly simplifying “3(x + 1) – 2” to “3x + 1″ without showing the steps can confuse the students, especially if they are just being introduced to algebra.

• #### Joseph Nebus 2:50 am on Wednesday, 29 April, 2015 Permalink | Reply

The double simplification is a problem, but I think it’s especially a problem that a 1 appears inside the parenthesis and then on the next line. That is, I think it’d be less confusing if they went from (say) “3(x + 3) – 2” directly to “3x + 7” since there’d be no suggestive-but-false connection between the number in parentheses and the number in the second line.

• #### ivasallay 8:20 am on Thursday, 30 April, 2015 Permalink | Reply

“x” looks a lot like a “+” if you roll it a little.
Students might like Brevity’s Venn diagram strip, so it could be a fun way to refresh their memories.

• #### Joseph Nebus 6:03 am on Tuesday, 5 May, 2015 Permalink | Reply

You know, I kept wondering whether the x should be considered a + in this case. It makes forming an equation a lot easier. I just feel like if it were meant to be a plus sign, then the character wouldn’t have feet coming out between two legs of the figure. (I hope you follow what I mean.) But the characters could probably roll over, if they wanted.

I think they use the term “cow tools” to describe the reaction the strip’s set off in me.

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