The Cardioid: Analytic Geometry
Channel: Kevin's Mathematical Musings
Date: 08/03/2021

Exploring the analytic geometry of the cardioid.

We derive polar and Cartesian formulae for the cardioid, study properties of its diameter, and compute its area and perimeter.

00:00 Introduction
00:56 Review
01:18 Analytic formula - polar coordinates
02:29 The diameter
03:47 Midpoints of diameters
04:23 Area of a cardioid
07:26 Perimeter of a cardioid
10:18 Summary
10:54 Coming attractions

Images:

René Descartes. Stipple engraving by W. Holl, after F. Hals, 1649. Credit: Wellcome Collection. Creative Commons Attribution 4.0 International (CC BY 4.0) https://creativecommons.org/licenses/by/4.0/

Microphone. 'rg1024' via https://openclipart.org/detail/20352/microphone. Creative Commons Universal Public Domain Dedication (CC0 1.0) https://creativecommons.org/publicdomain/zero/1.0/

Music:

'Almost New' Kevin MacLeod https://incompetech.com/ Licensed under Creative Commons: By Attribution 3.0 License http://creativecommons.org/licenses/by/3.0/