Background -- Maximizing Speed to Windward

Without Fancy Instruments

The picture to the left shows equal 4 triangles arranged in a square. The area of the square is C times C or C squared. The square is made up of the 4 triangles, each of which has an area of A times B divided by 2 or 2 times A times B in total. That leaves a small square in the center to be added to the 4 triangles to equal the area of the square. That little square is formed by the difference between side A and B so it has sides of length A minus B and an area equal to (A - B) times (A - B) which is A squared minus two A times B plus B squared. Combining that with the areas of the four triangles we get A squared plus B squared. QED.