On Fri, 16 Feb 2001 23:09:25 +0200, Peter Popov <pet### [at] vipbg> wrote:
>>It's been a long time, but try searching for "apolonian packing of
>>circles" at google or the like. You may have try try seaching on
>>variations on ap(p)ol(l)onian, I'm not sure of the spelling since it's
>
>Was it Marthin Gardner who had chosen a bachelor's thesis along the
>lines of "Optimal Packing of Equisized Spheres In 27-Dimensional
>Space"? It gets even odder... he provided diagrams :)

The appolonian packing of spheres isn't limited to equisized spheres
but adds smaller spheres in as many levels as levels as you have
patience for.

As for multi-dimensional math I remember some Linear Programming where
the solution plane is an n-1 dimensional plane intersecting the
n-dimensional variable space. The trick was finding the highest point
on that plane. At that time at had to run my models on a 4 MHz 8086
machine so big models took time. I rarely went above 20 dimensions but
they could take up to half an hour to solve (or infinity if there was
multiple solutions!). As I added more constraints the solution time
increased exponentially and when the models was getting complex enough
to be usefull they were too big to handle.

Erkki

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