Holditch's Ellipse Unveiled. Issue 5 (1st May 2017)

• Record Type: Journal Article
• Authors: Monterde, Juan; Rochera, David
• Is Part Of: American Mathematical Monthly. Volume 124:Issue 5(2017)
• Page Start: 403
• Page End: 421
• Publication Date: 2017-05-01
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.4169/amer.math.monthly.124.5.403
• Languages: English
• ISSNs: 0002-9890

Abstract

Abstract: 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 area is less than that of the original curve by π pq. In this article we obtain, first, sufficient conditions to ensure the existence of the Holditch curve and, second, a version of Holditch's theorem for convex polygons where the ellipse involved is explicitly shown.