A natural generalisation of
Pythagoras' theorem is to consider a
rightangled tetrahedron with four faces, three in mutually
perpendicular planes and one in the sloping plane. Then ask "what
corresponds to the squares of the lengths of the sides?"
The answer must be "the squares of the areas of the faces". If
these areas are $P$, $Q$ , $R$ and $S$ respectively then prove
that:
$P^2+ Q^2+ R^2= S^2$
