I never liked maths lessons when I was younger, but I do like origami. I've been making origami for fun for years, but I've only recently started learning that as well as being a fun creative pursuit, it can also function as a tool for solving problems in maths, just like the geometry you were taught at school.

The kind of geometry you usually learn at school is called "plane geometry". It's the geometry of flat surfaces, and it comes with its own set of rules, or axioms, which define how the system works, and what you can and can't do in order to solve problems. At school you usually learn about plain geometry through challenges where you're asked to solve some problem just using a drawing compass and a special unmarked ruler called a straight edge. Classic puzzles include how to split an angle or a line exactly in two, or how to draw a perfect equilateral triangle.

But guess what: straight edge and compass construction is just one of many ways to study geometry. We can explore all these problems and more using the solving power of a simple piece of paper ... no additional equipment needed!