This is a puzzle.
Lewis Carroll, the author of Alice in Wonderland, was also a mathematician. In his diary for 1890, he wrote the following statement:
is always the sum of two squares where x and y are a pair of non-zero integers.
Usually, when people want to see if Lewis Carroll was correct, they use algebra.
For this puzzle, I am going to ask you for a geometric argument to show whether Carroll’s result is correct.