What fraction is shaded?

# Category Archives: Written by others

# Semicircle Problem

Using s (for side of square), and/or r, for radius, what is the largest semi-circle you can inscribe in a square?

# Sangaku Problem #1

# mathschallenge.net student booklets

I’m a huge fan of the (now dormant, but still online) site mathschallenge.net

It’s full of excellent problems, and the author has organised them into 4 tiers of difficulty as pdfs here

However, the summary pdfs have the answers directly underneath each question, which isn’t ideal.

So I took the answers out for student versions here:

I use them a lot. The picture below shows printed a4 versions (with the answers) binded, and printed A5 versions (for students) without the answers, the A5 versions are the ones linked above.

# Circle Puzzle

A friend posted this on the maths staffroom notice board today. I like it!

I think it’s from an old UKMT paper.

# Circle & Square Problem

“Find a relationship between the square’s side s and circle’s radius R if Green Area = Red Area.”

Submitted by the very talented Derek Orr

# Old Exam Questions #7

First, my solution to Old Exam Question #6

I *think* I have a nice proof without words. I’m probably wrong. Incidentally I was wrong with last month’s solution. The corrected version is online now. I put the right angle in the wrong place. Oops.

Aaaanyway, here’s the next one from a Cambridge Maths Exam from 1918: