Origami

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

The first thing to notice when solving this problem is that the sides of a sheet of A4 paper are in the ratio $1$ to $\sqrt{2}$ . (Check this by taking a sheet and measuring it.)

It simplifies the working a great deal if we treat the sheet of A4 paper as a rectangle with sides $1$ and $\sqrt{2}$, and keep the working exact by leaving the square roots in our expressions rather than typing them into a calculator.

Published April 1998.