# One-bonacci, two-bonacci, three-bonacci...﻿May 12, 2018 7:52 AM   Subscribe

Beyond the golden ratio. How cutting your nails with scissors leads to the silver ratio, and the other "metalic ratios" and their place in nature. (slNumberphile)
posted by 445supermag (10 comments total) 27 users marked this as a favorite

I keep forgetting how good these are. Thanks for the post.
posted by Johnny Wallflower at 9:32 AM on May 12, 2018

...four, four-bonaccis make a bunch and so do many more...

Sorry, as you were.
posted by rory at 11:09 AM on May 12, 2018 [2 favorites]

I firmly believe we are being bamboozled here. the 3-bonacci sequence? the silver ratio?? I've never heard of these things before and I'm pretty sure a method of measurements based on cutting your fingernails is a vast hoax being perpetrated upon us.
posted by supermedusa at 11:27 AM on May 12, 2018 [1 favorite]

the word irrational is right in there!
posted by supermedusa at 11:29 AM on May 12, 2018

I was a little surprised they only generalized to

n = a * n(-1) + n(-2)

Where a = 1 is the Fibonacci. I was thinking you'd generalize to two variables:

n = a * n(-1) + b * n(-2)

Which might get you some weirder places.
posted by vibratory manner of working at 12:41 PM on May 12, 2018 [1 favorite]

The silver ratio is apparently popular in design in Japan, assuming video games didn't lie to me.
posted by jsnlxndrlv at 1:01 PM on May 12, 2018

For those interested in delving a little deeper, I wholeheartedly recommend this video on the topic by Infinite Series. It's another great channel for learning on topics of math (which, I must point, it's very different from actually learning mathematics but fun nonetheless)
posted by andycyca at 3:46 PM on May 12, 2018 [1 favorite]

I don't know, I think it's arguable that thinking about maths is the real maths, anything that involves manipulating symbols is just glorified arithmetic.

I admit that for those of us who aren't very good at that sort of symbol manipulation this may be seen as a convenient excuse, but look at all the things in nature (e.g., the falcon in this video) that do glorious maths without any symbol manipulation at all. Like, if I want a catenary curve I can make one with a bit of string; I wouldn't be able to depict one anywhere near as beautifully on a piece of paper, even if I were able to remember the formula – which I can't. But knowing about the curve is a way of thinking about the world. Just as a catenary curve is, mathematically, a way of thinking about the relationship between hyperbolas and straight lines, in architecture and nature it's a way of thinking about the relationship between gravity and tensile/compressive strength. It's analog thinking, not symbolic thinking, but I'd argue that it's a real thing and just as beautiful.
posted by Joe in Australia at 5:16 PM on May 12, 2018 [1 favorite]

There has been a run of Phi / Golden / Spiral / etc. recently on the few mathy youtube channels I follow. I forget exactly which bits the Nuberphile video covered, but here are a couple Mathologer videos along the same line.
The golden ratio spiral: visual infinite descent - YouTube
Infinite fractions and the most irrational number - YouTube
posted by zengargoyle at 9:15 PM on May 12, 2018 [1 favorite]

Since it has to do with fingernail clippings, shouldn't it be called the *sliver* ratio?
/ow
posted by notsnot at 10:31 AM on June 4, 2018 [1 favorite]

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