sphere's in ND space

General FreeBASIC programming questions.
bluatigro
Posts: 586
Joined: Apr 25, 2012 10:35
Location: netherlands

sphere's in ND space

Postby bluatigro » Mar 03, 2018 11:04

i got a problem for you :
how many sphere's fit around a sphere ?
in ND space ?
in 0D its simple : 0
in 1D its simple : 2
in 2D its simple : 6
but now in 3D : 12 , 14 or higher ?
[ in square piramid of sphere's 14 ]
i think you can calc this like this :
imaging 2 sphere's on eatch other
if you shine a holow sphere laser
to the certer of the center sphere
the other sphere casts a 'shadow'
on the center one
that 'shadow' has a 'arrya'
now is spheremax = spherearrya / 'arrya'
[ i don't know how to calc 'arrya' ]
spheremax is not the correct number of sphere's [?]
if not :
3 sphere's are on the center one and eatch other
these 3 sphere's make a 'triangle'
part of this 'triangle' is [shadow]
now t = 'tranlge'arrya and s = [shadow]arrya
number = spheremax * s / t
[ i dont know how to calc s and t ]

can anyone help me whit the formula's i missing ?
or show me the number ?

and how about in 4D ... ND ?
[ trangle and arrya wil be diferrent item's ]

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