THE PYTHAGOREANS: PYTHAGOREAN TRIANGLES & CIRCLES

“3D Thinking” Page 131: An animation of the Pythagorean Theorem shown dynamically in terms of circles. In the animation the diameter of the outer circle equals the hypotenuse of the right-angled triangle. The diameters of the two inner circles/spheres equal the lengths of the other two sides of the right-angled triangle. According to the Theorem of Pythagoras the sum of the surface areas of the two inner circles always equals the surface area of the outer circle/sphere. The animation rotates the right-angled corner of the triangle around the circumference of the outer circle. Pythagoras’ theorem states that the square of the hypotenuse (area) equals the sum of the squares (areas) of the other two sides….There’s a balance to the animation – a sort of harmony of proportion.