A circle is inscribed in an equilateral triangle. Smaller circles
touch it and the sides of the triangle, the process continuing
indefinitely. What is the sum of the areas of all the circles?
Gravity on the Moon is about 1/6th that on the Earth. A
pole-vaulter 2 metres tall can clear a 5 metres pole on the Earth.
How high a pole could he clear on the Moon?
Prove that if a is a natural number and the square root of a is
rational, then it is a square number (an integer n^2 for some