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)
...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]
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]
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
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]
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
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]
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]
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]
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]
/ow
posted by notsnot at 10:31 AM on June 4, 2018 [1 favorite]
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posted by Johnny Wallflower at 9:32 AM on May 12, 2018