Pythagorean Thm in 3D

Suppose we have a tetrahedron whose vertices are at the origin and the points given below:

[Graphics:../Images/index_gr_16.gif]

Then the square of the area of the face opposite to the origin is:

[Graphics:../Images/index_gr_17.gif]
[Graphics:../Images/index_gr_18.gif]

which is equal to the sum of the squares of the areas of the other sides.


Converted by Mathematica      September 20, 2001