Circles packed within a circle.

From: Bill Taylor (w.taylor_at_math.canterbury.ac.nz)
Date: 10/28/04 

Date: 27 Oct 2004 21:54:47 -0700

This must surely be well studied already?

It is desired to pack as many unit circles within a circle radius R >1 .
Non-overlapping of course, though they may be tangential.

Clearly for R < 2, only one circle will fit.

For R >=2, but less than some larger easily-calulable number,
2 circles is OK, but for R >= this, one can fit 3.

Similarly one may get 4 at some higher number; then 5.

BUT NOT 6 !
As soon as it becomes possible to fit six circles inside, it is already
possible to fit seven! There is no maximal pattern of six circles.

There are certain other numbers of circles which cannot be maximal numbers.

What is known about this in general?

------------------------------------------------------------------------------
        Bill Taylor W.Taylor@math.canterbury.ac.nz
------------------------------------------------------------------------------
Four circles to the kissing come.
The smaller are the benter.
The bend is just the inverse of
The distance from the centre.
Since zero bend's a dead straight line
And concave bends have minus sign,
The sum of the squares of all four bends
Is half the square of the sum.

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