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. . . .
Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?
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.
Go to last month's problems to see more solutions.
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.