German mathematician, David Hilbert (1862-1943), first proved that any polygon can be transformed into any other polygon of equal area by cutting it into a finite number of pieces.
This theorem is illustrated by one of the puzzles of the renowned English puzzlist, Henry Ernest Dudeney (1847-1930). Dudeney transforms an equilateral triangle into a square by cutting it into four pieces.
Here are four pieces. Fit them back together. First make them into an equilateral triangle and then into a square.