Make five different quadrilaterals on a nine-point pegboard,
without using the centre peg. Work out the angles in each
quadrilateral you make. Now, what other relationships you can see?
The length AM can be calculated using trigonometry in two different
ways. Create this pair of equivalent calculations for different peg
boards, notice a general result, and account for it.
On a nine-point pegboard a band is stretched over 4 pegs in a
"figure of 8" arrangement. How many different "figure of 8"
arrangements can be made ?
Join some regular octahedra, face touching face and one vertex of
each meeting at a point. How many octahedra can you fit around this
Stick some cubes together to make a cuboid. Find two of the angles
by as many different methods as you can devise.
Plane 1 contains points A, B and C and plane 2 contains points A
and B. Find all the points on plane 2 such that the two planes are
Neat proofs of two results about the golden ratio are demonstrated here.
Go to last month's problems to see more solutions.
How do you write a computer program that creates the illusion of stretching elastic bands between pegs of a Geoboard? The answer contains some surprising mathematics.