Ten squares form regular rings either with adjacent or opposite
vertices touching. Calculate the inner and outer radii of the rings
that surround the squares.
You can use a clinometer to measure the height of tall things that you can't possibly reach to the top of, Make a clinometer and use it to help you estimate the heights of tall objects.
Beautiful mathematics. Two 18 year old students gave eight
different proofs of one result then generalised it from the 3 by 1
case to the n by 1 case and proved the general result.