Let's play a few paper games. I will ask you to find a way to achieve something with paper using basic geometric knowledge (like a compass & ruler step by step process). The person to figure it out can propose his / her own problem. Then the person to solve that can do his / her own. (if it is unsolvable using only the given resources, then impossible is an acceptable answer) All the problems involve paper and its dimensions. Only the stated objects can be used. Got it? Let's begin.

--------------------------------------------------------------------------------------------------------------------------------

A simple one:

Materials: a letter size sheet of paper, and a ruler and protractor.

Conditions: The ruler only measures discretely, as in only 1 unit, 2 units, 3 units, etc. are labelled. You cannot measure a length other than the non-positive integers on the ruler. Folding is allowed.

Task: Create a length that you know is irrational.

Hint: It's a little tricky since you can't measure an irrational length with your ruler. So you'll have to make something you know is irrational based off the properties of what youcanmake. Pretty easy.