Comments on: The golden ratio has spawned a beautiful new curve: the Harriss spiral
http://www.metafilter.com/148950/The-golden-ratio-has-spawned-a-beautiful-new-curve-the-Harriss-spiral/
Comments on MetaFilter post The golden ratio has spawned a beautiful new curve: the Harriss spiralSat, 18 Apr 2015 20:12:12 -0800Sat, 18 Apr 2015 20:12:12 -0800en-ushttp://blogs.law.harvard.edu/tech/rss60The golden ratio has spawned a beautiful new curve: the Harriss spiral
http://www.metafilter.com/148950/The-golden-ratio-has-spawned-a-beautiful-new-curve-the-Harriss-spiral
<a href="http://www.theguardian.com/science/alexs-adventures-in-numberland/2015/jan/13/golden-ratio-beautiful-new-curve-harriss-spiral"> is a new fractal discovered by mathematician <a href="http://maxwelldemon.com/edmund-harriss/">Edmund</a> <a href="http://www.mathematicians.org.uk/eoh/"> Harriss</a>.</a>post:www.metafilter.com,2015:site.148950Sat, 18 Apr 2015 19:46:12 -0800boo_radleyharrissfractalphigoldenratiomathematicsscienceartphilosophyBy: wintersweet
http://www.metafilter.com/148950/The-golden-ratio-has-spawned-a-beautiful-new-curve-the-Harriss-spiral#6014571
I was so pleased when I first read about this, because it's nice to see good things come out of Arkansas/my alma mater sometimes. I realize Harriss isn't <em>from</em> Arkansas, but anyway: <a href="http://math.uark.edu">U of A math department</a>.comment:www.metafilter.com,2015:site.148950-6014571Sat, 18 Apr 2015 20:12:12 -0800wintersweetBy: trip and a half
http://www.metafilter.com/148950/The-golden-ratio-has-spawned-a-beautiful-new-curve-the-Harriss-spiral#6014583
Aw man, this is so beautiful. Make new math, but keep the old.comment:www.metafilter.com,2015:site.148950-6014583Sat, 18 Apr 2015 20:26:54 -0800trip and a halfBy: Mister Moofoo
http://www.metafilter.com/148950/The-golden-ratio-has-spawned-a-beautiful-new-curve-the-Harriss-spiral#6014598
Neato!
That "curvetile" doodad on his page (the "Hariss" link) is really nifty, too.comment:www.metafilter.com,2015:site.148950-6014598Sat, 18 Apr 2015 20:50:43 -0800Mister MoofooBy: kaibutsu
http://www.metafilter.com/148950/The-golden-ratio-has-spawned-a-beautiful-new-curve-the-Harriss-spiral#6014603
I met some jugglers this week who were talking about the problem of counting the number of ways you can throw a coin N times without having any steaks of length greater than k. The answer (after a good bit of thought) ended up being generalized Fibonacci numbers... Those wascally numbers seem to pop up everywhere...comment:www.metafilter.com,2015:site.148950-6014603Sat, 18 Apr 2015 20:58:51 -0800kaibutsuBy: kenko
http://www.metafilter.com/148950/The-golden-ratio-has-spawned-a-beautiful-new-curve-the-Harriss-spiral#6014616
<em>And now delete the largest arc, to reveal...a shape that I am going to call the "Harriss spiral".</em>
Why delete the largest arc? If it's left in every square is similar to every other; when it's deleted, one of them is unique.comment:www.metafilter.com,2015:site.148950-6014616Sat, 18 Apr 2015 21:15:51 -0800kenkoBy: Gymnopedist
http://www.metafilter.com/148950/The-golden-ratio-has-spawned-a-beautiful-new-curve-the-Harriss-spiral#6014625
Just in time for Bicycle Day!comment:www.metafilter.com,2015:site.148950-6014625Sat, 18 Apr 2015 21:32:19 -0800GymnopedistBy: el io
http://www.metafilter.com/148950/The-golden-ratio-has-spawned-a-beautiful-new-curve-the-Harriss-spiral#6014626
There are a disproportional amount of jugglers that are also mathematicians.comment:www.metafilter.com,2015:site.148950-6014626Sat, 18 Apr 2015 21:33:00 -0800el ioBy: oceanjesse
http://www.metafilter.com/148950/The-golden-ratio-has-spawned-a-beautiful-new-curve-the-Harriss-spiral#6014645
This seems like the sort of thing that would look better animated.comment:www.metafilter.com,2015:site.148950-6014645Sat, 18 Apr 2015 21:57:50 -0800oceanjesseBy: obiwanwasabi
http://www.metafilter.com/148950/The-golden-ratio-has-spawned-a-beautiful-new-curve-the-Harriss-spiral#6014676
This seems like the sort of thing that would attract unwanted attention from sleeping tentacled alien gods.comment:www.metafilter.com,2015:site.148950-6014676Sun, 19 Apr 2015 00:14:41 -0800obiwanwasabiBy: justsomebodythatyouusedtoknow
http://www.metafilter.com/148950/The-golden-ratio-has-spawned-a-beautiful-new-curve-the-Harriss-spiral#6014677
Beautiful mathematics repels tentacled alien gods.comment:www.metafilter.com,2015:site.148950-6014677Sun, 19 Apr 2015 00:24:04 -0800justsomebodythatyouusedtoknowBy: univac
http://www.metafilter.com/148950/The-golden-ratio-has-spawned-a-beautiful-new-curve-the-Harriss-spiral#6014694
So I'm the only one who thinks fractals are unattractive?comment:www.metafilter.com,2015:site.148950-6014694Sun, 19 Apr 2015 01:41:57 -0800univacBy: howfar
http://www.metafilter.com/148950/The-golden-ratio-has-spawned-a-beautiful-new-curve-the-Harriss-spiral#6014709
What is it with the Grauniad and the assertion that <s>π is exactly 3</s> the Golden Ratio "is 1.618"? That's not even a ratio.comment:www.metafilter.com,2015:site.148950-6014709Sun, 19 Apr 2015 02:53:18 -0800howfarBy: Wolfdog
http://www.metafilter.com/148950/The-golden-ratio-has-spawned-a-beautiful-new-curve-the-Harriss-spiral#6014713
In the same was that Fibonacci and Lucas sequences go along with the golden ratio, the Padovan (and Perrin) sequences go along with the "plastic constant" 1.3247... that appears in Harriss's construction. It's the root of x^3-x-1 instead of x^2-x-1.
A better-known "Padovan analog" of the golden spiral comes from <a href="http://en.wikipedia.org/wiki/Padovan_sequence#/media/File:Padovan_triangles_(1).png">spiraling equillateral triangles</a> instead of squares.comment:www.metafilter.com,2015:site.148950-6014713Sun, 19 Apr 2015 03:44:54 -0800WolfdogBy: Wolfdog
http://www.metafilter.com/148950/The-golden-ratio-has-spawned-a-beautiful-new-curve-the-Harriss-spiral#6014714
(27/2 - (3 sqrt(69))/2)^(1/3)/3 + ((9 + sqrt(69))/2)^(1/3)/3^(2/3) will probably never catch on the way (1+√5)/2 has, but to the connoisseur of algebraic numbers, it is at least as interesting as its more fêted relative.comment:www.metafilter.com,2015:site.148950-6014714Sun, 19 Apr 2015 03:51:51 -0800WolfdogBy: obiwanwasabi
http://www.metafilter.com/148950/The-golden-ratio-has-spawned-a-beautiful-new-curve-the-Harriss-spiral#6014717
<em>the Golden Ratio "is 1.618"? That's not even a ratio.</em>
It is understood that one side of the ratio is 1.618 times greater than the other. See Wikipedia: "<em>In general, a comparison of the quantities of a two-entity ratio can be expressed as a fraction derived from the <a href="http://en.wikipedia.org/wiki/Ratio">ratio</a>.</em>"
For example, pi is also an irrational number, yet people say that it is "<em>...<a href="http://en.wikipedia.org/wiki/Pi">the ratio of a circle's circumference to its diameter</a></em>" all the time.comment:www.metafilter.com,2015:site.148950-6014717Sun, 19 Apr 2015 03:59:48 -0800obiwanwasabiBy: Wolfdog
http://www.metafilter.com/148950/The-golden-ratio-has-spawned-a-beautiful-new-curve-the-Harriss-spiral#6014719
<small><strong>Corrections and Clarifications</strong>
Numerous readers have called our attention to the fact that the Golden Ratio is not, in fact, 1.618. Mathematicians now know that the Golden Ratio is 1.61803.</small>comment:www.metafilter.com,2015:site.148950-6014719Sun, 19 Apr 2015 04:14:07 -0800WolfdogBy: IAmBroom
http://www.metafilter.com/148950/The-golden-ratio-has-spawned-a-beautiful-new-curve-the-Harriss-spiral#6014743
<a href="http://www.metafilter.com/148950/The-golden-ratio-has-spawned-a-beautiful-new-curve-the-Harriss-spiral#6014709">howfar</a>: "<i>What is it with the Grauniad and the assertion that <s>π is exactly 3</s> the Golden Ratio "is 1.618"? That's not even a ratio.</i>"
You might consider suing your math teacher for negligence. $[+1-1+1-1...] would seem to be a fair amount.comment:www.metafilter.com,2015:site.148950-6014743Sun, 19 Apr 2015 05:18:56 -0800IAmBroomBy: Multicellular Exothermic
http://www.metafilter.com/148950/The-golden-ratio-has-spawned-a-beautiful-new-curve-the-Harriss-spiral#6014839
Why do I get the feeling that you can already find that spiral somewhere in the Book of Kells?comment:www.metafilter.com,2015:site.148950-6014839Sun, 19 Apr 2015 08:27:18 -0800Multicellular ExothermicBy: chavenet
http://www.metafilter.com/148950/The-golden-ratio-has-spawned-a-beautiful-new-curve-the-Harriss-spiral#6014852
<em>Corrections and Clarifications
Numerous readers have called our attention to the fact that the Golden Ratio is not, in fact, 1.618. Mathematicians now know that the Golden Ratio is 1.61803.</em>
´Course the <em>Grauniad</em> might call it the Gloden Ratio...comment:www.metafilter.com,2015:site.148950-6014852Sun, 19 Apr 2015 08:43:57 -0800chavenetBy: sciurus
http://www.metafilter.com/148950/The-golden-ratio-has-spawned-a-beautiful-new-curve-the-Harriss-spiral#6014864
This reminds me of <a href="http://korsh.com/cfdg/">Context Free Design Grammar</a>.comment:www.metafilter.com,2015:site.148950-6014864Sun, 19 Apr 2015 08:52:45 -0800sciurusBy: nobody
http://www.metafilter.com/148950/The-golden-ratio-has-spawned-a-beautiful-new-curve-the-Harriss-spiral#6014930
<i>Why delete the largest arc? If it's left in every square is similar to every other; when it's deleted, one of them is unique.</i>
I'd guess it's because that largest arc dead-ends at the edge of the frame, unlike all the others, and he/they decided it would be nicer without that dead-end implying the infinitely larger shape what's being drawn might as well be considered a part of?comment:www.metafilter.com,2015:site.148950-6014930Sun, 19 Apr 2015 10:26:27 -0800nobodyBy: wreckingball
http://www.metafilter.com/148950/The-golden-ratio-has-spawned-a-beautiful-new-curve-the-Harriss-spiral#6014944
Why do I get the feeling that you can already find that spiral in someone's regrettable late-nineties armband tattoo?comment:www.metafilter.com,2015:site.148950-6014944Sun, 19 Apr 2015 10:47:04 -0800wreckingballBy: quin
http://www.metafilter.com/148950/The-golden-ratio-has-spawned-a-beautiful-new-curve-the-Harriss-spiral#6014971
<em>This seems like the sort of thing that would attract unwanted attention from sleeping tentacled alien gods.</em>
Sorry, I was having lunch... someone called?
Oh, hey! Lovely bit of curvature there. In my language that means "Eat the squishies." Weird how these things work out, isn't it?comment:www.metafilter.com,2015:site.148950-6014971Sun, 19 Apr 2015 11:16:07 -0800quinBy: not_that_epiphanius
http://www.metafilter.com/148950/The-golden-ratio-has-spawned-a-beautiful-new-curve-the-Harriss-spiral#6015015
Phine bit of design.comment:www.metafilter.com,2015:site.148950-6015015Sun, 19 Apr 2015 12:08:32 -0800not_that_epiphaniusBy: sour cream
http://www.metafilter.com/148950/The-golden-ratio-has-spawned-a-beautiful-new-curve-the-Harriss-spiral#6015205
<em>The blue rectangle and the orange rectangle have the same proportions as the overall rectangle, which is a ratio between the sides of 1.325.</em>
He's totally lost me here.
What blue rectangle is he talking about?
All rectangles are clearly white and gold.comment:www.metafilter.com,2015:site.148950-6015205Sun, 19 Apr 2015 14:24:11 -0800sour creamBy: TreeRooster
http://www.metafilter.com/148950/The-golden-ratio-has-spawned-a-beautiful-new-curve-the-Harriss-spiral#6015366
Hey, <a href="http://www.metafilter.com/user/17619"><strong>Wolfdog</strong></a> and other mathy types, what do you think the chances are that the conjecture in the article is right--that every algebraic number can be found as the ratio of the sides of a rectangle which can be subdivided into squares and similar rectangles? Seems like a pretty deep result, if true, and the counterexamples would be interesting even if not.comment:www.metafilter.com,2015:site.148950-6015366Sun, 19 Apr 2015 18:31:46 -0800TreeRoosterBy: Wolfdog
http://www.metafilter.com/148950/The-golden-ratio-has-spawned-a-beautiful-new-curve-the-Harriss-spiral#6015805
I really don't know. It doesn't seem far-fetched to me, and it also doesn't seem particularly deep, at first whiff; I would not be surprised if you can find a systematic way of building a rectangle pattern based on the minimal polynomial for the algebraic number (although there are some caveats (which are more than I'm going to go into during my short lunch break between 4th grade and 5th grade math (my life is pretty weird at the moment))). On the other hand, I mucked around trying to come up with a rectangle/square pattern for (the dominant root of) x^4-x^3-1 and I concluded that you do need to be systematic; just mucking around is a little too mucky.comment:www.metafilter.com,2015:site.148950-6015805Mon, 20 Apr 2015 07:56:10 -0800WolfdogBy: larrybob
http://www.metafilter.com/148950/The-golden-ratio-has-spawned-a-beautiful-new-curve-the-Harriss-spiral#6016168
Makes me think of a couple of other fractals: The <a href="http://en.wikipedia.org/wiki/Dragon_curve">Dragon Curve</a> and the <a href="http://en.wikipedia.org/wiki/L%C3%A9vy_C_curve">Lévy C curve</a>.comment:www.metafilter.com,2015:site.148950-6016168Mon, 20 Apr 2015 11:24:53 -0800larrybobBy: pjenks
http://www.metafilter.com/148950/The-golden-ratio-has-spawned-a-beautiful-new-curve-the-Harriss-spiral#6016707
That number, 1.3247..., has another name: the <a href="https://books.google.com/books?id=E7S02uF81u4C&pg=PA266&lpg=PA266&dq=%22spiral+mean%22+cubic&source=bl&ots=uqH1eHKMUp&sig=l9NuM3fqTg4cEcY5UXjh-FnngEs&hl=en&sa=X&ei=tf41VduCEZC1sQSq24HQCA&ved=0CDAQ6AEwAw#v=onepage&q=%22spiral%20mean%22%20cubic&f=false">spiral mean</a>.
The golden mean plays a very important role in physics and the mathematics of dynamical systems. In the transition from order (i.e., integrability) to chaos, it is the frequency ratio for orbits on the torus (T^2) that make the torus most robust to perturbations. The fact that it represents the last outpost of order is related to it being the "most irrational" number (in the sense of its <a href="http://en.wikipedia.org/wiki/Continued_fraction">continued fraction expansion</a>).
From the perspective of dynamics, the spiral mean is thought, by some, to be the analog of the golden mean in higher-dimensional dynamical systems (dynamics on T^3). And, in some generalizations of the continued fraction, it is "most irrational".comment:www.metafilter.com,2015:site.148950-6016707Tue, 21 Apr 2015 01:09:49 -0800pjenks