April 2020 - mathfun@mailman.xmission.com

Re: [math-fun] Fibonacci/Golden Ratio in Art
by Steve Witham 27 Apr '20

27 Apr '20

Here's an animation that runs in recent Chrome, Firefox and Safari at least: http://www.mac-guyver.com/switham/2014/02/Meristem/ There's are links there to a set of 3 Vi Hart videos about spirals in plants, S. Douady and Y. Couder's magnetized oil drop experiment video, and Â "The Mathematical Lives of Plants," by Julie J. Rehmeyer. Â --Steve

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Re: [math-fun] Fibonacci/Golden Ratio in Art
by Stuart Anderson 26 Apr '20

26 Apr '20

I enjoyed the skeptical approach to the appearance of phi in art and nature taken by Donald Simanek in this article https://www.lockhaven.edu/~dsimanek/pseudo/fibonacc.htm Then I read Michael Trott's big data analysis of aspect ratios in paintings. Perhaps phi does have some artistic relevance after all. https://blog.wolfram.com/2015/11/18/aspect-ratios-in-art-what-is-better-tha… On Mon, Apr 27, 2020, 04:00 <math-fun-request(a)mailman.xmission.com> wrote: > Send math-fun mailing list submissions to > math-fun(a)mailman.xmission.com > > To subscribe or unsubscribe via the World Wide Web, visit > https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun > or, via email, send a message with subject or body 'help' to > math-fun-request(a)mailman.xmission.com > > You can reach the person managing the list at > math-fun-owner(a)mailman.xmission.com > > When replying, please edit your Subject line so it is more specific > than "Re: Contents of math-fun digest..." > > > Today's Topics: > > 1. Re: Fibonacci/Golden Ratio in Art (Hilarie Orman) > > > ---------------------------------------------------------------------- > > Message: 1 > Date: Sun, 26 Apr 2020 11:53:56 -0600 > From: "Hilarie Orman" <ho(a)alum.mit.edu> > To: math-fun(a)mailman.xmission.com > Subject: Re: [math-fun] Fibonacci/Golden Ratio in Art > Message-ID: <202004261753.03QHru26021460(a)rumpleteazer.rhmr.com> > > Does it matter if the artist is aware of the math? Perhaps the > question should be why there is an irrational number that approximates > a parameter for the human visual system: > > https://www.theguardian.com/artanddesign/2009/dec/28/golden-ratio-us-academ… > But I don't think anything beyond the tenths place matters, visually. > > Helaman Ferguson's sculptures are the most masterful combinations of > art and math that I've seen. Complete awareness. > > Ruth McDowell created a superb Fibonacci quilt: > https://www.internationalquiltmuseum.org/quilt/20080400227 > She has many other quilts with mathematical themes. > > The artistic representation of phi is one of the persistent themes of > Gathering for Gardner. > > I would like to see (hear, taste, feel) more art that represents math, > even at the expense of the artistic aesthetic. I'd like to have the > balance point shifted towards math. > > Some artists working early in the twentienth century felt influenced > by developments in physics, allegedly. I never understood that in > any way other than a feeling of being free to investigate radically > new ideas. It would have been more interesting if the physicists had > felt free to express their research in art, rather than the other > way round. > > > Furthermore, many (if not most) of the supposed findings > > of phi (the Golden ratio) in art are spurious coincidences, > > without any shred of evidence that the artist knew anything > > about golden ratios. > > > > A big problem is finding images/sculptures/animations > > that are both interesting/fun to look at, but also provide > > interesting/fun mathematical/geometric insights. > > Hilarie > > > > > ------------------------------ > > Subject: Digest Footer > > _______________________________________________ > math-fun mailing list > math-fun(a)mailman.xmission.com > https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun > > > ------------------------------ > > End of math-fun Digest, Vol 206, Issue 66 > ***************************************** >

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[math-fun] Kerala to Kumbakonam
by Brad Klee 26 Apr '20

26 Apr '20

Surely it has already been speculated that the practice of familial transmission of scientific knowledge could have descended ideas about Pi through a geopolitical (georeligious?) spacetime web from Madhava to Ramanujan, especially considering the small distance between Kerala and Kumbakonam. Undoubtedly this would be a difficult evolutionary process to trace (impossible if oral histories are the only evidence and lost). I am currently searching for references or anecdotes. Are any already known to the funsters? see also: https://www.youtube.com/watch?v=lseuvdal5t8 --Brad

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[math-fun] {(x,y,z): x+y+z=0}
by James Propp 26 Apr '20

26 Apr '20

I’ve spent 10 minutes googling things like “triangular coordinates“ and “reduced barycentric coordinates“ but haven’t found what I’m looking for. So, apologies if you feel I should have googled longer instead of wasting funsters’ time, but maybe one of you will instantly know the name of the coordinate system in which points in the plane are represented by triples summing to zero (and more generally n-tuples summing to zero in higher dimensions). Actually, I might as well include a followup question, which is, where is the best place to look for translations of the standard high school formulas for coordinate geometry into this somewhat arcane coordinate system? I could spend an hour figuring them out for myself, but that’s an hour I’d rather spend figuring out something new, and more importantly, I might make mistakes! Thanks, Jim Propp

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[math-fun] Fact-free trivia game
by James Propp 25 Apr '20

25 Apr '20

About 30 years ago my friends Bruce Smith and Dan Ullman and I shared a bank of seats on a plane, and played a game in which the questions are Fermi problems and the goal of each guesser on a given turn is to guess the MEDIAN of the three guesses. (Any odd number of odd people can play.) Did we invent this? Jim

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[math-fun] Another Proof on Edwards’s curves
by Brad Klee 24 Apr '20

24 Apr '20

Earlier this year we were talking about Kepler’s laws, and I had some seemingly stupid idea about how to make it less easy to understand. This purportedly bad idea grew into a whole paper: https://github.com/bradklee/Dissertation/blob/master/Prelude/Prelude.pdf (The in-line reader does not always work, but “download” does) Most notably, section VII contains a short proof, less than a page, for certifying the ODE of EllipticK (in Cartesian coordinates). I have not seen it, or anything like it, so maybe it is new. There are other interesting ideas in there, including a tabulation of Core results, the definition of “Hotaru mirabilis” (not mentioned at all in OEIS, completely excluded), and a simplification of the proof of Legendre’s relation, compare with: https://math.stackexchange.com/questions/701515/proving-legendres-relation-… This is not exactly self-promotion, but more of a call to the naysayers. If they have any rational reason why it shouldn’t be published, they could say so now! I am thinking of putting it up on arxiv with tags for physics and algebraic geometry, but I am sure that would ruffle some feathers. So, any thoughts? —Brad

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Re: [math-fun] Physically intuitive?
by Keith F. Lynch 24 Apr '20

24 Apr '20

Brad Klee <bradklee(a)gmail.com> wrote: > The same day I found three species of Onthophagus, I also found an > Alaus oculatus (the largest Elateridae I have seen in situ) near a > rather large gallery of Bess beetles. While I was handling it, it > snapped at me, and the power of it surprised me completely! Latch mechanisms aside, small creatures tend to produce more power per unit mass and per unit volume. Power is limited by the ability to take in oxygen and to eliminate carbon dioxide and heat. And, over the longer term, also by the ability to take in food and eliminate waste. This is done through their surfaces, and is used or generated through their volumes, so creatures with a small ratio of volume to surface area can produce more power per mass. A small ratio of volume to surface area goes with a creature that is small in one, two, or all three dimensions (i.e. flat, long and skinny, or just overall small). This applies to things other than animals. For instance the sun, which has an astonishingly low power output per kilogram -- four or five orders of magnitude less than a person! The sun's surface is hot only because there's so much volume behind every square meter of its surface. The sun's fuel has far more energy per kilogram than human fuel, but the sun's (primordial) breakfast has to fuel it for billions of years, while your breakfast only need fuel you until lunch. It's been pointed out that if the Star Wars Death Star generates heat at the same rate per volume as an average office building, it would have to be white hot to radiate away all the waste heat. (There's no convective or conductive heat loss in the vacuum of space, only radiative.) No wonder it blew up. It's also been pointed out that whole world's human population could fit into a cubical building about two kilometers on a side. True, but there's only one place in the solar system with enough cooling capacity to keep everyone from soon dying of heatstroke. The building would have to be situated in the mouth of the Amazon River. Plenty of places, on and off Earth, are much colder than that tropical river, but none of them have that much moving fluid with that high a specific heat. According to my calculations, the river would be heated by just one degree Celsius, not counting waste heat from whatever machinery in the building keeps everyone fed, entertained, etc. Getting back to the subject line, one of my hobbies is collecting un-intutive facts.

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[math-fun] Physically intuitive?
by Bill Gosper 23 Apr '20

23 Apr '20

In[395]:= UnitConvert[Quantity[42, "Watts"], "Kilograms" "Meters"^2/"Seconds"^3] Out[395]= Quantity[42, ("Kilograms" ("Meters")^2)/("Seconds")^3] This seems to say: If you apply a given amount of power (to a freely moving object) for twice as long, you go eight times as far. —rwg

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[math-fun] Ex. What Not To Do.
by Brad Klee 21 Apr '20

21 Apr '20

Screen Cap: https://0x0.st/i1zI.png of Fig. 4.4 from: https://scholarworks.uark.edu/etd/2456/ Look how horrible these _published_ fits are! This is a U of A certified Physics PhD, in fact, certified by the two people whose sole decision it was to make me a victim of the March purge, against the best wishes of my committee. The histograms themselves are asymmetric, but the fit function is a symmetric Gaussian. Instead of rushing ahead to incorrectly repeat standard blah-blah-blah, if that's all they can do after so many years, looks like the author needs to stop and ask "WTF?" or "What's The Function?" If the author is still ignorant to this day, maybe it would be a good idea to study the recently released "Summer Insect Pandemics": https://demonstrations.wolfram.com/SummerInsectPandemicsInTheUnitedStates/ Sorry, but this is much better data analysis, which accounts for asymmetry. It's not even for a PhD, it's just for fun and to cope with stress of being treated like an insect by these "big shot" faculty members! --Brad PS. Where are the error bars on extracted parameters? What about covariance? etc. etc...

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[math-fun] Conway's heptagon construction
by Bill Gosper 20 Apr '20

20 Apr '20

(neusis) <http://www.tweedledum.com/rwg/heptagon.htm> —rwg

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