Hi Bill, I have just been playing with a circle and and a hypocycoid, and
imploding a circle:
load '~addons/graphics/fvj4/dwin.ijs'
do=: 13 :'({.y) +(i.{:y)*(--/ 2{.y)%<:{:y'
circle=:|: 2 1 o. /t=:do 0 2p1 81
_1 _1 1 1 dwin 'dwin polar circle'
200 0 200 dpoly circle
hypo=:|:(2 1 o./t=:do 0 2p1 81)^3
_1 _1 1 1 dwin 'dwin polar hypocycloid'
200 0 50 dpoly hypo
whatif=:|:(2 1 o./t=:do 0 2p1 81)^2
NB.whatif=:|:2 9$1 0.5 0 0.5 1 0.5 0 0.5 1 0 0.5 1 0.5 0 0.5 1 0.5 0
_1 _1 1 1 dwin 'dwin polar whatif'
50 0 200 dpoly (*hypo)*whatif
Linda
-----Original Message-----
From: Programming [mailto:[email protected]] On Behalf
Of bill lam
Sent: Tuesday, August 15, 2017 10:42 PM
To: [email protected]
Subject: Re: [Jprogramming] "n-volume" of an "n-sphere"
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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> >
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--
regards,
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