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.