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!

Some problems that take a bit of thought using the straight edge and construct approach are trivial to solve using origami. For example, bisecting a line can be as easy as folding a sheet of paper in half!

Origami geometry still deals with flat surfaces, but it actually offers an extended problem solving tool kit, simplifying some problems, and making others that were previously impossible into genuinely solvable problems.

In this lesson I'll show you how to use origami to solve the problem of dividing a square of paper into thirds, and then I'll show you how to construct an algebraic proof to demonstrate that this technique really works.

Along the way we'll learn or refresh some fundamentals in maths:

properties of triangles

quadratic equations

rearranging equations

You can work through this lesson just by looking at the diagrams on screen, but you may find it more interesting if you grab a square of paper and follow along in real life. You can usually buy specially made squares of origami paper from craft stores, or you can make your own square using this simple technique.

Try lesson one for free:

You can sample lesson two here: