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
Each pentagon has a turn of 36o to pack against its
Therefore it will take 10 (x36o) turns to complete a
full-turn, i.e. 10 pentagons
Therefore 7 more pentagons are needed.
This problem is taken from the UKMT Mathematical Challenges.