#47 Squares and circles
Set by Katie Steckles
A circle is drawn so it touches the sides of a square, and then the largest square that fits is drawn inside the circle.
What is the ratio between the area of the small square and large square? (Hint: you might find it useful to rotate the inner square.)
Consider the larger square and the circle. How many copies of the circle do you need to completely cover the square?
With a nod to the late mathematician David Singmaster, who wrote a paper based on this problem: which fits better – a…
