An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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?
Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP
have equal areas. Prove X and Y divide the sides of PQRS in the
This is the only solution of the equation for which x and y are whole numbers. Another way of looking at this is to say that 26 is the only whole number "sandwiched" between a perfect square and a perfect cube. This was proved by the French mathematician, Pierre de Fermat, in the 17th Century.
This problem is taken from the UKMT Mathematical Challenges.