If one considers a point as infinitesimal -as usually considered-, then
we have an infinite number of points at an infinitesimal distance from
the origin and at a larger distance from the origin there are still an
infinite number of points on the surface and an infinite number of
points enclosed . Isn't this getting into transfinite math?
What's the point?
Don Kelly
On 2017-08-15 8:23 PM, Jimmy Gauvin wrote:
The construction of the sphere implies it cannot be convex but you will
have to find a topologist to prove it to you.
The sphere is the collection of points whose distance to the origin is
equal to the radius of the sphere.
The ball or volume is comprised of the points whose distance to the origin
is equal or smaller than the radius of the sphere.
On Tue, Aug 15, 2017 at 10:41 PM, bill lam <[email protected]> wrote:
Has the n-sphere become concave in higher dimension?
Вт, 15 авг 2017, Jimmy Gauvin написал(а):
Funny how the n-Sphere volume dwindles for the higher dimensions.
Not quite intuitive but the factorial always "win" even with bigger
radii.
The hypercubes do not share this characteristic (V= edge ^ n)
On Tue, Aug 15, 2017 at 3:33 PM, Ben Gorte - CITG <
[email protected]>
wrote:
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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