Liu Hui’s Visual Proof of the Pythagorean Theorem (after Dauben’s Reconstruction)
The right triangle is determined by vertices ABC
In Liu Hui’s visual proof, the colored pieces can be rearranged to cover the regions outside the overlapping area—either outside the large square or outside the two smaller squares
What does this show about the relationship between the three squares?
A. The overlap is the same in both figures, so the areas can be compared.
B. Certain areas outside the overlap between the squares are equal, showing that the total area of the two smaller squares equals that of the large one.
C. The pieces change shape slightly, so the areas can be adjusted.
D. The large square is always bigger than each small square, so the theorem follows.