Holditch's theorem
id:
holditch-s-theorem-290-7836630
title:
Holditch's theorem
text:
In plane geometry, Holditch's theorem states that if a chord of fixed length is allowed to rotate inside a convex closed curve, then the locus of a point on the chord a distance p from one end and a distance q from the other is a closed curve whose enclosed area is less than that of the original curve by π p q . The theorem was published in 1858 by Rev. Hamnet Holditch. While not mentioned by Holditch, the proof of the theorem requires an assumption that the chord be short enough that the traced
brand slug:
wiki
category slug:
encyclopedia
description:
On the area enclosed by a point on a rigid chord rotating inside a convex closed curve
original url:
https://en.wikipedia.org/wiki/Holditch%27s_theorem
date created:
date modified:
2023-02-10T08:18:59Z
main entity:
{"identifier":"Q1888583","url":"https://www.wikidata.org/entity/Q1888583"}
image:
{"content_url":"https://upload.wikimedia.org/wikipedia/commons/6/64/Holditch_s_theorem.svg","width":921,"height":461}
fields total:
13
integrity:
15