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
Let AB have length 3r. The distance moved by A is then the
circumference of a semicircle radius 3r (3$\pi$r). C moves along a
circle of radius 2r (2$\pi$r), followed by a semicircle of radius r
($\pi$r). The total distance moved by C is therefore also 3$\pi$r.
This problem is taken from the UKMT Mathematical Challenges.