question-of-the-day answered

[Kurt Cockrum]

Rich said:
>Solution needed.
>
>If I have a styrofoam ball one foot in diameter, how can I find the
>precise location of the opposing poles?

Suspend the ball from a thread attached to the eye of a needle driven
into the sphere, and lower it until it touches the ground, plumbob style.
It will touch at a point more or less antipodal to the point of suspension.

Another thing to try is to make 2 tangent cones that match at their perpendicular
bases.  The sphere will be securely contained within the two joined cones.
Then a line going from the apex of one cone to the other apex will pierce
a diameter of the sphere.  Try a hot coat-hanger.  A CO2 laser bore-sighted
along the apices would make the work easy.  This could also be the basis for
a drill-press fixture that would hold the sphere for drilling.  Rather than the
cones, an open-air design using tripods that bolt together, caging the sphere,
might be a workable design.

Lastly, try a tangent equilateral tetrahedron, with the bottom side missing. 
Put it over the sphere.  A line from the top vertex to where the sphere touches
the ground will pass thru the center of the sphere.
--kurt
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