Ask the Chatbot Games & Quizzes History & Society Science & Tech Biographies Animals & Nature Geography & Travel Arts & Culture ProCon Money Videos
torus
References
Images
A diagram of a torus with a highlighted circular cross-section and labeled distances a and b from the center, illustrating how Pappus's Theorem is used to calculate the torus's volume.
Britannica AI Icon

torus

mathematics
Written by
The Information Architects of Encyclopaedia Britannica

The Information Architects maintain a master list of the topics included in the corpus of  Encyclopædia Britannica, and create and manage the relationships between them.
The Information Architects of Encyclopaedia Britannica
Last updated

Quick Summary

A diagram of a torus with a highlighted circular cross-section and labeled distances a and b from the center, illustrating how Pappus's Theorem is used to calculate the torus's volume.
Pappus's theorem

Pappus's theorem proves that the volume of the solid torus obtained by rotating the disk of radius a around line L that is b units away is (πa2) × (2πb) = 2π2a2b cubic units.

In mathematics, a torus is a doughnut-shaped surface generated by rotating a circle around an axis in its plane that does not intersect the circle. This shape is also referred to as a toroid.1

Pappus's theorem provides a way to calculate the volume of a torus. It states that the volume of a solid generated by revolving a plane region is equal to the product of the area of that region and the distance traveled by its centroid during the revolution. For a torus formed by rotating a circle of radius a around an axis b units away from its center, the volume is calculated as (2\pi^2 a^2 b) cubic units.2

Summary created from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles.
3 Britannica Sources
  1. torus
  2. Pappus’s theorem
  3. tori

Ask Britannica AI about this topic

Britannica doesn't have a full article on this topic, so we've curated a list of our relevant coverage.