i^2 = j^2 = k^2 = ijk = -1. This deceptively simple formula, discovered by Irish mathematician William Rowan Hamilton in 1843, led to a revolution in the way 19th century mathematicians and scientists thought about vectors and rotation. This formula, which extends the complex numbers, allows us to talk about certain three-dimensional problems with more ease. So what are quaternions? Where are they still used? And what is inscribed on Broom Bridge? All of this and more on this episode of Breaking Math.

This episode is distributed under a CC BY-SA 4.0 license. For more information, visit CreativeCommons.org.

The theme for this episode was written by Elliot Smith.

[Featuring: Sofía Baca, Meryl Flaherty]