Can you prove that the sum of the distances of any point inside a square from its sides is always equal (half the perimeter)? Can you prove it to be true for a rectangle or a hexagon?

A moveable screen slides along a mirrored corridor towards a centrally placed light source. A ray of light from that source is directed towards a wall of the corridor, which it strikes at 45 degrees. . . .

Draw a line (considered endless in both directions), put a point somewhere on each side of the line. Label these points A and B. Use a geometric construction to locate a point, P, on the line,. . . .

Draw a square and an arc of a circle and construct the Golden rectangle. Find the value of the Golden Ratio.

Find a connection between the shape of a special ellipse and an infinite string of nested square roots.

Find the link between a sequence of continued fractions and the ratio of succesive Fibonacci numbers.

Curt produced a clear demonstration of the fundamental result he wanted to use to proof the proposed relationship.

An iterative method for finding the value of the Golden Ratio with explanations of how this involves the ratios of Fibonacci numbers and continued fractions.

A voyage of discovery through a sequence of challenges exploring properties of the Golden Ratio and Fibonacci numbers.

This game is known as Pong hau k'i in China and Ou-moul-ko-no in Korea. Find a friend to play or try the interactive version online.