Largest spheres found in dimensionality near five and a quarter.
Beautiful mathematics, and need string theory limit itself to integral dimensions?
boxdraw_j_ 1 load'~addons/math/misc/amoeba.ijs' sphvol=: (1p1&^%!)@-:@] * ^ g=: -@:(1&sphvol) g amoeba(<16)Y=:2 1$4.1 5.8 +-------+--------+ |5.25692|_5.27777| +-------+--------+ On 08/16/2017 08:00 AM, [email protected] wrote:
Date: Tue, 15 Aug 2017 19:33:09 +0000 From: Ben Gorte - CITG<[email protected]> To:"[email protected]" <[email protected]> Subject: Re: [Jprogramming] "n-volume" of an "n-sphere" Message-ID: <[email protected]> Content-Type: text/plain; charset="us-ascii" A little surprise (to me) was plot 1 sphvol i.30 (for example) Can you predict it? greetings, Ben ________________________________________ From: Programming [[email protected]] on behalf of Raul Miller [[email protected]] Sent: Tuesday, August 15, 2017 19:55 To: Programming forum Subject: [Jprogramming] "n-volume" of an "n-sphere" sphvol=: (1p1&^%!)@-:@] * ^ 1 sphvol 3 4.18879 1 sphvol i.7 1 2 3.14159 4.18879 4.9348 5.26379 5.16771 Left argument is the radius of the "n-sphere". Right argument is the number of dimensions. I put "n-volume" in quotes, because if the dimension is 2 (for example), the "n-volume" is what we call the area of the circle. (And if the dimension is 1 that "n-volume" is the length of a line segment). Anyways, I stumbled across this and thought it might be interesting for someone else. Thanks, -- Raul
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