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The Art of π, φ and e
June 26, 2012 2:27 PM   Subscribe

The Art of π, φ and e

The creator of Circos and hive plots plays around with visualizing a few irrational numbers and their odd characteristics.
posted by Blazecock Pileon (24 comments total) 12 users marked this as a favorite

 
very pretty but I didn't understand a bit of it. Are I stupid?
posted by Uncle Grumpy at 2:45 PM on June 26, 2012


The beauty of these numbers lies in their mathematical meaning, which can and has been exploited in art and nature in many ways, and many ways no doubt remain to be explored. However, the representation of the distribution of their decimal expansions is arguably no more aesthetically interesting than that of any random series of digits.
posted by iotic at 2:49 PM on June 26, 2012 [15 favorites]


However, the representation of the distribution of their decimal expansions is arguably no more aesthetically interesting than that of any random series of digits.

Worse still, because pi is probably normal, there shouldn't be any special pattern to which digits follow which other digits. So we wouldn't expect the first visualization to reveal anything interesting.
posted by Jpfed at 3:04 PM on June 26, 2012 [7 favorites]


Those particular visualizations didn't really do anything for me, but they did remind me of something very cool: the continued fraction representation for e. And hey, there's even a nice pattern you can get for pi if you generalize continued fractions a bit.
posted by kmz at 3:04 PM on June 26, 2012 [3 favorites]


However, the representation of the distribution of their decimal expansions is arguably no more aesthetically interesting than that of any random series of digits.

I don't think it has to be more interesting in order to be interesting.
posted by shakespeherian at 3:10 PM on June 26, 2012


It's as interesting as snow on the TV, which I have to admit I did like watching as a kid.
posted by escabeche at 3:58 PM on June 26, 2012 [1 favorite]


I think I can see Alan Turings face in the "Distribution of the first 13,689 digits of π."
posted by sammyo at 3:59 PM on June 26, 2012 [2 favorites]


aggh. This is making my head hurt :)
[in an interesting way]
posted by twidget at 4:01 PM on June 26, 2012


Oh so pretty. I keep telling my tutoring students that math is elegant and beautiful, and they keep insisting it is ugly and meaningless. I felt that way too, being forced to learn it. But now, as an adult, I find it so lovely.
posted by strixus at 4:53 PM on June 26, 2012


In fact all these pictures should look, when you squint, exactly the same.

(Continued fraction versions of these visualizations would be more interesting.)
posted by madcaptenor at 5:11 PM on June 26, 2012


It's as interesting as snow on the TV, which I have to admit I did like watching as a kid.

Me too. I was also a bit of a pyromaniac and accidentally burned off part of our back porch, and I've always thought those two things were probably connected.

The appearance of a pattern in the continued fraction for e, whereas π seems not to have one, has always puzzled me.

Both numbers are often said to have "random" decimal expansions, but could the patterned CF make e less random than π by some construction of randomness that took both into account?
posted by jamjam at 5:12 PM on June 26, 2012


MY BRAIN HURTS

Hey, remember string art? *goes and makes some string art*
posted by Sys Rq at 5:14 PM on June 26, 2012 [1 favorite]


Hey! πφe was my college fraternity!

We were the geekiest fraternity on campus until they started e + 1.
posted by twoleftfeet at 5:17 PM on June 26, 2012 [1 favorite]


Pfffft. e + 1. That's nothing.
posted by maryr at 6:03 PM on June 26, 2012 [12 favorites]


There is a nice explanation of Exotic R^4 via slice knots on mathoverflow, although you'll need some topology knowledge to decipher it.

Exotic R^4s always freaked me out : It's a smooth manifold homeomorphic but not diffeomorphic to R^4, alright sounds strange but pathologies happen. Yeah, except this pathology cannot happen for R^n with n ≠ 4!
posted by jeffburdges at 6:06 PM on June 26, 2012


You kids have it so easy. When I was young, you had to turn the Spirograph disk yourself. With a crappy ball point pen! And the pen usually tore a hole through the paper before you were done, or the disk skipped a cog and your picture was ruined.
posted by not_on_display at 6:36 PM on June 26, 2012 [2 favorites]


He's got a surprising amount of art based on the distribution of digits in these numbers - superimposing them on top of each other, making a new number out of the numbers where the digits match. It such a bizarre thing to fixate on.

It's like counting the brush strokes in the Mona Lisa, making dozens of art projects based on that particular number, and titling them "Visualizing the Painting Process of the Mona Lisa."
posted by straight at 8:41 PM on June 26, 2012


Previously.
posted by neuron at 9:10 PM on June 26, 2012 [1 favorite]


That there is little discernable difference between the three plots of e, Pi, Theta respectively, illustrates just how arbitrary these are. I'm sure that the decimal expansion of root 2, or any number of irrational numbers would look pretty much exactly the same.

Since this is purporting to show the "beauty of these universal constants" in particular then yes it is necessary show that it is not entirely the plotting method that is responsible for the "beauty".

I want to see a similar plot of a say a generic random number generator for comparison.

This has a similar pointlessness as those "visualisations" or musical "interpretations" of astronomic data from pulsars that you see picked up all over the web.
posted by mary8nne at 3:33 AM on June 27, 2012 [2 favorites]


Does it bother anyone besides me that φ is not transcendental? (In fact, it's [√5 ± 1]/2). That suggests to me that any set of irrational numbers would behave in the same way.
posted by ubiquity at 7:04 AM on June 27, 2012 [1 favorite]


I'll be more interested when someone does one of these for ii. (Hint: It's a real number)

Not that the visualization would be any different, but the expression would screw with people's brains sufficiently.
posted by Hactar at 7:15 AM on June 27, 2012


I'll be more interested when someone does one of these for ii. (Hint: It's a real number)

BIG Hint: It's e-π/2.
posted by ubiquity at 8:03 AM on June 27, 2012


jamjam: The appearance of a pattern in the continued fraction for e, whereas π seems not to have one, has always puzzled me.
Were you aware of this series, developed by Euler?
π = 1 + 1/2 + 1/3 + 1/4 - 1/5 + 1/6 ...

The rule for the signs (+/-) are left as a googlable exercise for the reader.
posted by IAmBroom at 8:33 AM on June 27, 2012


curiously ASN(π, φ, e) ≈ 1

Someone truly brave as John Keel or Richard Hoagland could tell us why.
posted by Twang at 2:02 PM on June 27, 2012


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