Kevin Heffern
Further solutions, most of them not entirely complete, were submitted
by Courtney Pelowski, Kristin Hellem, Steven Goggins, Corey Kinsman, Eric
Baldwin, Kristina Rogers, Joe Thornton. Further solutions were submitted
by Ahmed Aboadham, Alejandro Vellano, Iñigo Picaza, Al Zimmermann,
Nancy Schwarzkopf, Paul Botham, Dane Brooke, Lou Cairoli, Sudipta Das,
Francesc Suñol y Esquirol, Bill Webb.
The
radius, oA, of the circle is 1/2. The angle BoA
is p/4, or 45°. degrees. As a result, the
length of CD equals the length of oE. The function
describing the height CD as a function of the length of the arc
AC depends on your choice of coordinates, of course. Choosing
to place the origin at the point A, we get a description given by
| Height function | = CD |
| = oE | |
| = 1/2 cos q | |
| = 1/2 cos 2(q/2) | |
| = 1/2 cos (arclength(AC)) | |
| = 1/2 cos x. |
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