>My primary question is: If you put a tetrahedron inside a
>sphere in such a way that the four points of the tetrahedron
>are on the surface of the sphere, what would be the
>lattitude on the sphere that the three points at the base of
>the tetrahedron would share. I could calculate this myself
>but I don't know the required formulas so here are some
>other questions about the formulas.

You can certainly do it yourself. Assume the tetrahedron has the base ABC and the apex S. Let Q be center of ABC, AQ extended intersect BC in K. Let O be the center of the sphere. If the side of the tetrahedron is 1,

AK = sqrt(3)/2,
SK = sqrt(3)/2,
in triangle SQK, Q is right,
QK = AQ/3,
use the pythagorean theorem in SQK to find SQ,
SO = SQ·3/4,
AO = SO,
in triangle AOS, find angle O by the theorem of cosines.

>
>I know that the surface formula for a sphere equals 4*p*r2.
>Is p the length of the perimeter (equator)?

p is the famous constant p, which is approximately 3.14...