One crucial aspect of mathematics often doesn’t involve numbers at all: the study of shape, and the symmetries of shapes and patterns, forms the important mathematical field of geometry. As well as 2D and 3D shapes, it includes higher-dimensional objects and infinite tiling patterns.

Topology is a more abstract way to study shapes, considering only their fundamental properties, the number of holes. We can apply it to real physical shapes, but also to abstract shapes like data sets, to identify the shapes made by trends and correlations.

Geometry also links to functions – conic sections describe shapes made by slicing through a cone, but also link to trigonometry. Vectors describe motion in space, and have their own ...

Get Math 100 Ideas in 100 Words now with the O’Reilly learning platform.

O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.