Pythagorean Theorem
RandomInstance can be used to create visual representations of geometric theorems. The Pythagorean theorem is a fundamental theorem in Euclidean geometry that states that for any right triangle with leg lengths 
and 
and hypotenuse 
, 
.
Visualize the Pythagorean theorem in terms of the areas of the squares based on each side of a right triangle.
A beautiful visual proof is to inscribe a square of side length 
in a square of side length 
in such a way that each vertex of the inner square divides a side of the outer square into two segments of length 
and 
.
Indeed, the area of the large square can be calculated in two ways.
The area of the outer square is the square 
of its side length 
, yielding 
.
Alternatively, the inner square has area 
, and each of the four triangles has area 
, so the area of the large square is 
, which is 
.
Hence 
, so 
.
