Mathematics

As almost everything in nature, we can define a set of mathematical rules, so-called axioms and theorems, in order to express in a precise way what paper-folding means. These mathematical rules can later be applied into other sciences, by simply using the results that mathematics proves. Mathematics is a powerful tool that it can substitute a ruler and compass! Ruler and compass cannot trisect an angle or double the cube. However, origami can, since both problems are equivalent to solving cubic equations. Origami can also be used in optimization, for example in finding the biggest triangle inside a square, or even solving the perimeter problem.