Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I want to read more about the amazing result that, when given a closed, convex curve in the plane that can be traversed internally by a chord of length $p$+$q$, and on that chord lying at p, a point, the path of which traces another curve inside the first, the area between these curves is $\pi$$p$$q$.

I have forgotten the name of this result. Haddart? I can't seem to find it. If someone knowns what I mean, please reveal.

share|improve this question

1 Answer 1

up vote 2 down vote accepted

This is taken from Pickover's "The Math Book"

Draw a smooth, closed, convex curve $C_1$. Place a chord of constant length inside curve $C_1$, and let the chords slide around the curve so that the two ends of the chord touch $C_1$ at all times. Label a point on the stick so that it divides the stick into two parts of length $p$ and $q$. As you move the stick, the point traces out a new closed curve $C_2$ within the original curve. Assuming that $C_1$ is shaped in such a way that the stick can actually pass around $C_1$ once, Holditch's theorem states the area between the curves $C_1$ and $C_2$ will be $\pi qp$. Interestingly, this area is totally independent of the shape of $C_1$.

share|improve this answer
    
Yes, that's it! Thanks. –  Cris Stringfellow Feb 21 '13 at 8:35

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.