Holditch's theorem

In plane geometry, Holditch's theorem states that if a chord of fixed length is allowed to rotate around 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 \pi pq.

Observations

The theorem is included as one of Clifford Pickover's 250 milestones.[1] Some peculiarities of the theorem include that the \pi pq area is independent of the shape of the original curve, and that the area's form matches that for the area of an ellipse. The theorem's author was a president of Caius College, Cambridge.

References

  1. ^ Pickover, Clifford (1 September 2009), The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics, Sterling, ISBN 978-1-4027-5796-9 

External links