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Holditchs theorem - Wikipedia Holditch's theorem 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
Holditchs Theorem - from Wolfram MathWorld Provided certain conditions are met, the area between C and C^' is given by pipq, as first shown by Holditch in 1858 The Holditch curve for a circle of radius R is another circle which, from the theorem, has radius r=sqrt (R^2-pq)
On Holditch’s theorem | Journal of Geometry - Springer In this paper we present a certain modification of the Holditch construction This construction allows to consider a geometric family of pairs of ring domains It is proved that the ratio of areas of ring domains of each pair belonging to this family is constant
Holditchs Theorem - JSTOR In order to make explicit the assumptions Holditch apparently made, and to clarify the conditions under which his theorem holds, we wish to carefully restate the theorem
HOLDITCH’S ENVELOPE - mathres. org As Holditch, we assume to start with a convex simple curve that bounds a compact convex region Furthermore, the curve is said to be Ck-regular on an open interval if it is k times continuously differentiable with nonvanishing derivative on that interval