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dansmath — circle blink
#circles #math #mathart #mathgif
Published: 2016-12-19 17:36:26 +0000 UTC; Views: 323; Favourites: 2; Downloads: 0
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Description
Forty-one colorful circles narrow into ellipses and back again, in perfect concert. Is 41 the sum of two squares? Drawn in Mathematica and exported as a GIF. Or is it a JIF?Related content
Comments: 2
4^2 + 5^2. Oh, I guess that's indicated in your graphic.
There's also 21^2 +(20i)^2.
You've heard of the sequence of primes starting with 41?
41, 43, 47, 53, 61, 71, 83, etc. The sequence continues until it is broked by 1681. And 1681 is 41^2. Looks like 61 is the sum of two squares.
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Thanks for replying. And as I write this, today is a Pythagorean day! 12/20/16, 12^2 + 16^2 = 20^2.
Yes, your primes starting at 41 are output value of x^2 + x + 41, x=0, 1, 2, 3, ..., 39. Good one!
(and spoiler: every prime that's 1 more than a multiple of 4 is the sum of two squares!)
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