

The golden ratio has spawned a beautiful new curve: the Harriss spiral - bootload
http://www.theguardian.com/science/alexs-adventures-in-numberland/2015/jan/13/golden-ratio-beautiful-new-curve-harriss-spiral

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Chinjut
As a mathematician, I was all ready to be dismayed by or dismissive of the
article, as with almost all popular discussion of mathematics (and
particularly so with the reams of nonsense which have been written in the past
about "the golden ratio"), but I was pleasantly surprised to find it
reasonably well written and interesting. Hoorah!

[I do wish it hadn't linked at the end to this twaddle about the golden ratio
governing women's peak fertility through their uterus dimensions...]

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proee
We have some ferns in our yard that have similar curves. Curious to know what
other nature forms take this on.

[https://s-media-cache-
ak0.pinimg.com/236x/9d/0a/36/9d0a365fd...](https://s-media-cache-
ak0.pinimg.com/236x/9d/0a/36/9d0a365fda002822f2ca8359bae6fc9a.jpg)

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HCIdivision17
That's a really spiffy connection you found.

I wonder what modification to the Harriss curve is needed to make it so that
it only curves inward? (I had been hoping to see if he goes more in-depth on
the process, but his site's sorta dying). It might be entertaining to fool
with it a bit in Processing and see what comes out.

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T-hawk
Why do we delete the largest arc? I couldn't understand the elegance of the
spiral until seeing that that had been done. Deleting that largest arc breaks
the self-similarity. Without it, the topmost scale becomes an S curve and
doesn't match the smaller layers of branching curves. I looked at the first
image for around a minute trying to find the S curves in the lower layers to
establish the self-similarity.

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zem
i like it - it looks more plantlike with the largest arc deleted

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drcode
Hmm... I have to say, I'm a little underwhelmed by both the aesthetics and the
technical construction of this particular curve, but who am I to complain
about the aesthetics of another man's fractal.

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boyaka
Made me think of the trisquel logo, although that is apparently related to
many other historical symbols and is probably less math and more design.

[http://trisquel.info/en/wiki/logo](http://trisquel.info/en/wiki/logo)

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pcrh
Some are uncannily similar to Celtic knots.

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CapitalistCartr
It looks very Dr. Seuss.

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dudifordMann
So... he applied an L-system to a Fibonacci -spiral? I suppose that's
innovative.

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ajkjk
I don't understand this kind of dismissal. So what if he did?

Maybe the innovation is considering this kind of thing as art again when it's
passe.

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arjn
Very interesting and pretty ... and it does remind me of Celtic art.

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chii
it looks surprisingly similar to a dragon curve

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jbob2000
"Duuude, what if instead of cutting a square, we cut a rectangle?"

"No way maaann! Unheard of!"

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DanielStraight
You mock, but this kind of tinkering is basically the foundation of
mathematics.

I suggest reading Lockhart's Lament, linked on this Wikipedia page:
[https://en.wikipedia.org/wiki/A_Mathematician%27s_Lament](https://en.wikipedia.org/wiki/A_Mathematician%27s_Lament)

Relevant quote:

> For example, if I’m in the mood to think about shapes— and I often am— I
> might imagine a triangle inside a rectangular box. I wonder how much of the
> box the triangle takes up? Two-thirds maybe? The important thing to
> understand is that I’m not talking about this drawing of a triangle in a
> box. Nor am I talking about some metal triangle forming part of a girder
> system for a bridge. There’s no ulterior practical purpose here. I’m just
> playing. That’s what math is— wondering, playing, amusing yourself with your
> imagination.

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Udo
Aside from its style, this seems like a valid criticism. How trivial can a
permutation be and still be sufficiently interesting for someone to
(justifiably) slap his name on it? That said, this was still a nice read and
the guy is obviously having fun with it, so good for him.

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Gelada
In this case the change is significant. If you just cut squares you can do
quite a bit and it leads to significant ideas related to continued fractions,
but you will only get finite continued fractions (rational numbers) and
periodic ones (quadratic numbers). Cutting rectangles and squares can give
higher degree algebraic numbers, like the cubic number for the main spiral. I
am working on a porrf that you can get all algebraic numbers.

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lubujackson
This isn't remotely new information?

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DanBC
Where has the Harriss spiral appeared before?

