## Any Requests?

I’m thinking to do a second Mathematics A-To-Z Glossary. For those who missed it, last summer I had a fun string of several weeks in which I picked a mathematical term and explained it to within an inch of its life, or 950 words, whichever came first. I’m curious if there’s anything readers out there would like to see me attempt to explain. So, please, let me know of any requests. All requests must begin with a letter, although numbers might be considered.

Meanwhile since there’s been some golden ratio talk around these parts the last few days, I thought people might like to see this neat Algebra Fact of the Day:

People following up on the tweet pointed out that it’s technically speaking wrong. The idea can be saved, though. You can produce the golden ratio using exactly four 4’s this way:

If you’d like to do it with eight 4’s, here’s one approach:

And this brings things back around to how Paul Dirac worked out a way to produce any whole number using exactly four 2’s and the normal arithmetic operations anybody knows.

## Christopher Adamson 3:06 pm

onSaturday, 30 January, 2016 Permalink |How about A is for axiom?

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## Joseph Nebus 4:18 pm

onSaturday, 30 January, 2016 Permalink |Happy to. I’ll set it on the list.

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## Christopher Adamson 4:56 am

onSunday, 31 January, 2016 Permalink |Yes!

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## KnotTheorist 8:48 pm

onSaturday, 30 January, 2016 Permalink |I enjoyed last year’s Mathematical A-To-Z Glossary, so I’m glad to see you’ll be doing another one!

I’d like to see C for continued fractions.

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## Joseph Nebus 12:39 am

onTuesday, 2 February, 2016 Permalink |Continued fractions … mm. Well, I’ll have to learn more about them, but that’s part of the fun of this. Thank you.

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## davekingsbury 6:29 pm

onSunday, 31 January, 2016 Permalink |Energy = Mass times Twice the Speed of Light … or is that more like Physics?

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## Joseph Nebus 12:40 am

onTuesday, 2 February, 2016 Permalink |is physics, although it’s something that we learned from mathematical considerations. And a big swath of mathematics is the study of physics. There’s a lot to talk about in energy for mathematicians.

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## elkement (Elke Stangl) 7:38 am

onMonday, 8 February, 2016 Permalink |Of course I second that :-) What about explaining a Lagrangian in layman’s terms? ;-)

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## Joseph Nebus 5:27 am

onWednesday, 10 February, 2016 Permalink |You know, I think I’ve got a hook on how to explain that. It might even get to include a bit from my high school physics class.

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## davekingsbury 9:14 am

onTuesday, 2 February, 2016 Permalink |Is the equation based on theory or is there a practical mathematics behind it?

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## Joseph Nebus 12:03 am

onWednesday, 3 February, 2016 Permalink |I’m not sure what you mean by theory versus practical mathematics. The energy-mass equivalence does follow, mathematically, from some remarkably simple principles. Those amount to uncontroversial things like the speed of light being a constant, independent of the observer, and that momentum and energy are conserved.

It

isexperimentally verified, though. We can, for example, measure the mass of atoms before and after they fuse, or fission, and measure the amount of energy released or absorbed as light in the process. The amounts match up as expected. (That’s not the only test to run, of course, but it’s an easy one to understand.) So the reasoning isn’t just good, but matches what we see in the real world.LikeLike

## davekingsbury 10:36 am

onWednesday, 3 February, 2016 Permalink |Thanks for your clear explanation. I’m not a scientist. Theory wasn’t the right word, then – I was thinking of empirically verifiable which your 2nd paragraph shows. Are the ‘uncontroversial things in your first paragraph also measurable in the real world?

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## Joseph Nebus 8:34 pm

onFriday, 5 February, 2016 Permalink |OK. Well, these are measurable things, in that experiments give results that are what we would expect from the assumptions, and that are inconsistent with what we’d expect from alternate assumptions. For example, we now assume the speed of light (in a vacuum) to be constant. That followed a century of experimentation that finds it does appear to always be constant, and it’s consistent with tests that look to see if there might be something surprising now that we have a new effect to measure or a new tool to measure with. Assumptions about, for example, the way that velocities have to add together in order for this constant-speed-of-light to work have implications for how, say, moving electric charges will produce magnetic fields, and we see magnetic fields induced by moving electric charges consistently with that.

We can imagine our current understanding to be incomplete, and that the real world has subtleties we haven’t yet detected. But I’m not aware of any outstanding mysteries that suggest strongly that we’re near that point.

So, given assumptions that seem straightforward enough, and that match experiment as well as we’re able to measure, physicists and mathematicians are generally inclined to say that these assumptions are correct. Or at least correct enough for the context in which they’re used. This is starting to get into the philosophy of science and the concept of experimental proof and gets, I admit, beyond what I’m competent to discuss with authority.

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## davekingsbury 8:43 pm

onFriday, 5 February, 2016 Permalink |Thanks for taking the time (and space) to explain this so clearly and enjoyably to a rookie. No more questions, promise … for now!

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## Gillian B 5:39 am

onWednesday, 3 February, 2016 Permalink |Isomorphism.

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## Joseph Nebus 8:12 pm

onFriday, 5 February, 2016 Permalink |Ooh, a challenging one. I’ll give it a try, though.

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## How January 2016 Treated My Mathematics Blog | nebusresearch 3:01 pm

onWednesday, 3 February, 2016 Permalink |[…] Any Requests? […]

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## Reading the Comics, February 6, 2016: Lottery Edition | nebusresearch 12:44 am

onMonday, 8 February, 2016 Permalink |[…] Any Requests? […]

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## gaurish 7:00 am

onMonday, 8 February, 2016 Permalink |Normal subgroup (easy one) or Number (difficult one, Bertrand Russell tried it once).

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## Joseph Nebus 5:24 am

onWednesday, 10 February, 2016 Permalink |Oh, number is easy. Three, for example, is the thing that’s in common among Marx Brothers, blind mice, tricycle wheels, penny operas, and balls in the Midnight Multiball of the pinball game FunHouse. Normal subgroup, now that’s hard.

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## gaurish 7:10 am

onMonday, 8 February, 2016 Permalink |Transcendental numbers; Dedikind Domain; matrix; polynomial; quartenions; subjective map; vector.

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## Joseph Nebus 5:26 am

onWednesday, 10 February, 2016 Permalink |There’s some good challenges here! My first reaction was to say I didn’t even know what a Dedekind domain was, although in looking it up I realize that I must have learned of them. I just haven’t thought of one in obviously too long, and I like the chance to learn something just in time to explain it.

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## elkement (Elke Stangl) 7:40 am

onMonday, 8 February, 2016 Permalink |C as Conjecture. More of a history of science question: When is an ‘unproven idea’ honored by being called a conjecture?

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## Joseph Nebus 5:35 am

onWednesday, 10 February, 2016 Permalink |Conjecture may work, yes, and fit neatly against axiom trusting that I use that.

I’m not sure there is a clear guide to when an unproven idea gets elevated to the status of conjecture. I suspect it would defy any rationally describable process. I mean about getting regarded as a name-worthy conjecture. There’s conjectures in much mathematical literature and those tend to mean the person writing the paper got a hunch that something might be so, but didn’t have the time or ability to prove it and is happy to let someone else try.

But to be, let’s say, the Stangl Conjecture takes more. I suspect part is that it has to be something that feels likely to be true, and which has some obviously interesting consequence if true (or false). That can’t be all, though. The Collatz Conjecture, as I’ve mentioned, seems to be nothing but an amusing trifle. But then that’s also a conjecture that’s very easy for anyone to understand, and it has some beauty to it. The low importance of it might be balanced by how much fun it seems to be and how everyone can be in on the fun.

I’ll have to do some more poking around famous conjectures, though, and see if I can better characterize what they have in common.

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## Dice and Compass Games | nebusresearch 3:04 pm

onSaturday, 13 February, 2016 Permalink |[…] with that hook, I’d like to toss in one last appeal for any requests for the Winter 2016 Mathematics A To Z. Before you pull out calendars on me and work out how long three-a-week essays might last, remember […]

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## A Leap Day 2016 Mathematics A To Z: Axiom | nebusresearch 3:02 pm

onMonday, 29 February, 2016 Permalink |[…] Any Requests? […]

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## elkement (Elke Stangl) 7:30 am

onTuesday, 1 March, 2016 Permalink |Equation or Differential Equation, depending on which letter is still open. I am thinking of the way THE FORMULA is depicted in movies, and I believe that it might imply that anything with an equal sign in it is more like Ohm’s Law – a ‘formula’ you just have to plug numbers into. I am sure you can explain the difference between a simple formula and a differential equation nicely :-) Or use Formula instead if F has not been taken.

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## Joseph Nebus 8:57 pm

onTuesday, 1 March, 2016 Permalink |Hm. I may take you up on differential equation, since the first nominee — Dedekind domains — is taxing my imagination. And I’d slid continued fractions over to F … but I will think about whether I can find a way to put Formula in under another letter.

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## How February 2016 Treated My Mathematics Blog | nebusresearch 9:18 pm

onTuesday, 1 March, 2016 Permalink |[…] Any Requests? […]

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## A Leap Day 2016 Mathematics A To Z: Conjecture | nebusresearch 3:01 pm

onFriday, 4 March, 2016 Permalink |[…] decided to address that by putting ‘Fractions, continued’ on the roster. If you have other requests, for letters not already committed, please let me know. I’ve got some letters I can use […]

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## Jacob Kanev 11:54 pm

onFriday, 4 March, 2016 Permalink |First things that tumble into my mind: Itô integral, Stratonovitch integral, Kulbach-Leibler divergence, Fisher information, Turing machine, Church’s lemma (is this the correct term in English? And you have ‘C’ already, haven’t you?), grammars (both context sensitive and not), Girsanov transformation (sorry for using ‘G’ twice), filtration (I’d really like a good explanation of this one) (and ‘F’), Banach spaces. Orthogonal. Projection. Distance. Metric. Measure. NP-completeness? Gödel’s theorem? Laws of form (that calculus by George Spencer Brown)?

Might be too nichey, though. You decide.

Lots of regards, Jacob.

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## Joseph Nebus 7:36 am

onWednesday, 9 March, 2016 Permalink |Well, wow. I do have a couple of these letters taken already — I’ve got through ‘F’ penciled in, plus a couple such as ‘I’ taken after that. But I’ll try to get as many of these as I can done in a coherent form. It’s going to be an exciting month ahead.

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## A Leap Day 2016 Mathematics A To Z: Dedekind Domain | nebusresearch 3:00 pm

onMonday, 7 March, 2016 Permalink |[…] this season’s A To Z open to requests I figured I’d get some surprising ones. So I did. This one’s particularly challenging. It comes fro Gaurish Korpal, author of the Gaurish4Math […]

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## A Leap Day 2016 Mathematics A To Z: Energy | nebusresearch 3:00 pm

onWednesday, 9 March, 2016 Permalink |[…] Another of the requests I got for this A To Z was for energy. It came from Dave Kingsbury, of the A Nomad In Cyberspace blog. He was particularly intersted in how E = mc2 and how we might know that’s so. But we ended up threshing that out tolerably well in the original Any Requests post. So I’ll take the energy as my starting point again and go in a different direction. […]

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## A Leap Day 2016 Mathematics A To Z: Fractions (Continued) | nebusresearch 3:00 pm

onFriday, 11 March, 2016 Permalink |[…] request! I was asked to write about continued fractions for the Leap Day 2016 A To Z. The request came from Keilah, of the Knot Theorist blog. But […]

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## A Leap Day 2016 Mathematics A To Z: Grammar | nebusresearch 3:01 pm

onMonday, 14 March, 2016 Permalink |[…] next entry for this A To Z was another request, this one from Jacob Kanev, who doesn’t seem to have a WordPress or other blog. (If I’m mistaken, please, let me […]

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## A Leap Day 2016 Mathematics A To Z: Isomorphism | nebusresearch 3:00 pm

onFriday, 18 March, 2016 Permalink |[…] Gillian B made the request that’s today’s A To Z word. I’d said it would be challenging. Many have been, so far. But I set up some of the work with “homomorphism” last time. As with “homomorphism” it’s a word that appears in several fields and about different kinds of mathematical structure. As with homomorphism, I’ll try describing what it is for groups. They seem least challenging to the imagination. […]

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## A Leap Day 2016 Mathematics A To Z: Kullbach-Leibler Divergence | nebusresearch 3:00 pm

onWednesday, 23 March, 2016 Permalink |[…] mathematics glossary term is another one requested by Jacob Kanev. Kaven, I learned last time, has got a blog, “Some Unconsidered Trifles”, for those […]

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## A Leap Day 2016 Mathematics A To Z: Matrix | nebusresearch 3:01 pm

onMonday, 28 March, 2016 Permalink |[…] I get to start this week with another request. Today’s Leap Day Mathematics A To Z term is a famous one, and one that I remember terrifying me in the earliest days of high school. The request comes from Gaurish, chief author of the Gaurish4Math blog. […]

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## A Leap Day 2016 Mathematics A To Z: Normal Subgroup | nebusresearch 3:03 pm

onWednesday, 30 March, 2016 Permalink |[…] The Leap Day Mathematics A to Z term today is another abstract algebra term. This one again comes from from Gaurish, chief author of the Gaurish4Math blog. Part of it is going to be easy. Part of it is going to need a running start. […]

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## A Leap Day 2016 Mathematics A To Z: Orthonormal | nebusresearch 3:04 pm

onFriday, 1 April, 2016 Permalink |[…] Jacob Kanev had requested “orthogonal” for this glossary. I’d be happy to oblige. But I used the word in last summer’s Mathematics A To Z. And I admit I’m tempted to just reprint that essay, since it would save some needed time. But I can do something more. […]

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## A Leap Day 2016 Mathematics A To Z: Polynomials | nebusresearch 3:01 pm

onMonday, 4 April, 2016 Permalink |[…] have another request for today’s Leap Day Mathematics A To Z term. Gaurish asked for something exciting. This should be less challenging than Dedekind Domains. I […]

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## A Leap Day 2016 Mathematics A To Z: Quaternion | nebusresearch 3:12 pm

onWednesday, 6 April, 2016 Permalink |[…] I’ve got another request from Gaurish today. And it’s a word I had been thinking to do anyway. When one looks for mathematical terms starting with ‘q’ this is one that stands out. I’m a little surprised I didn’t do it for last summer’s A To Z. But here it is at last: […]

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## A Leap Day 2016 Mathematics A To Z: Surjective Map | nebusresearch 4:04 pm

onMonday, 11 April, 2016 Permalink |[…] Gaurish today gives me one more request for the Leap Day Mathematics A To Z. And it lets me step away from abstract algebra again, into the world of analysis and what makes functions work. It also hovers around some of my past talk about functions. […]

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## A Leap Day 2016 Mathematics A To Z: Transcendental Number | nebusresearch 3:00 pm

onWednesday, 13 April, 2016 Permalink |[…] down to the last seven letters in the Leap Day 2016 A To Z. It’s also the next-to-the-last of Gaurish’s requests. This was a fun […]

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## A Leap Day 2016 Mathematics A To Z: Vector | nebusresearch 3:04 pm

onMonday, 18 April, 2016 Permalink |[…] And as we approach the last letters of the alphabet, my Leap Day A To Z gets to the lats of Gaurish&… […]

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