Essay On Origami

Sha Tin College

SL Mathematics

Internal Assessment

Alexander Zalivin

The Mathematics of Origami

Nov 2014

Introduction

Origami is an ancient art of folding paper and people usually associate it with paper planes or birds that children play with. However, the study of origami isn’t only a study of paper folding, as there are various mathematical aspects to it. Origami can be applied to the study of calculus, geometry, and even abstract algebra. Perhaps, origami could be a substantial key to the mathematical comprehension for some students.

Originally origami came from China (known as Zhe Zhi in Mandarin) however, with time it became more popular in Japan, so it is mainly considered a Japanese art. There are even different types of paper used to make origami.

By inventing new folds and models they are continually contributing valuable information to the

field of mathematics.

Relation between origami and mathematics

As origami works with paper to produce various geometric shapes, therefore it can be compared with geometry. Similarly to geometry, origami has a set of postulates, which are almost like geometrical theorems axioms. There are seven of them and Humiaki Hutuza, a nuclear scientist, developed the first six; later Jacques Justin found the seventh postulate.

Postulate 1: ‘Given two points P1 and P2, one can fold a single crease which passes through them.’

The evidence of similarity between this postulate and Euclid’s first postulate, ‘through any two distinct points, it is possible to draw (exactly) one straight line’ is quite obvious.

Postulate 2: ‘Given two points P1 and P2, one can fold a crease placing P1 onto P2.’

This is related to the construction of a perpendicular bisector of a line segment. Placing point P1 on point P2 creates a crease folded perpendicularly to the midpoint of the straight line P1P2; the intersection point becomes the bisector.

Postulate 3: ‘Given two lines L1 and L2, one can fold a crease placing L1 onto