---
title: torus
permalink: torus
date: 2023-05-17T11:30:27-07:00
tags: math
---

One of my favorite mathematical shapes is the torus. Not only does it remind me
of a doughnut (mmm), but it's the first step into topology with the introduction
of a hole. Not only is a doughnut topologically a torus, but so is your
accompanying coffee mug[^1]!

![torus-mug-donut](../media/855427377f7b5a4f.webp)

But where does this word _"torus"_ come from? It happens to be the Latin word
for... a pillow. The classic round poof with a pin through the middle to keep it
flat[^2].

![torus](../media/a1084b7c72c13d71.png)

Later used to describe architectural decoration that reminded them of that
shape, in particular the rounded molding at the base of some Doric columns.

![torus-column](../media/611e56ceb553030d.jpg)

I find it fascinating how words we consider academic and sterile have roots in
everyday things. "That column base looks like a fluffy pillow, let's call it so"
led to a defined term as mathematics provided architectural rigor.

[^1]:
    This homeomorphism famously leads dedicated topologists to confuse their mug
    for their doughnut. Classic messy situation.

[^2]: Pillows lack a hole and are decidedly a non-toroidal "torus".