Can you express every recurring decimal as a fraction?
Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?
A square of area 40 square cms is inscribed in a semicircle. Find the area of the square that could be inscribed in a circle of the same radius.
Let a(n) be the number of ways of expressing the integer n as an ordered sum of 1's and 2's. Let b(n) be the number of ways of expressing n as an ordered sum of integers greater than 1. (i) Calculate a(n) and b(n) for n<8. What do you notice about these sequences? (ii) Find a relation between a(p) and b(q). (iii) Prove your conjectures.
An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?
The area of a square inscribed in a circle with a unit radius is 2. What is the area of these other regular polygons inscribed in a circle with a unit radius?
Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?
A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?
Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?
Can you work out the fraction of the original triangle that is covered by the inner triangle?
