Let *S* be an arc on the portion of the unit circle which lies
in the first quadrant.
Let *A* be the area under *S* and above the
*x*-axis, let *B* be the area to the left of *S*
and to the right of the *y*-axis.
Show that *A*+*B* depends only on the length of
*S* and not on its position.

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Rules:
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- Answers must be written neatly on 8.5 by 11 inch paper.
- Answers must be submitted to Dr. Buchanan either at his office (Wickersham 113) or placed in his department mailbox by the department secretary.
- The contest will open on July 20, 1998.
- The first complete and correct answer will be awarded the sum of $5.00 (five US dollars).
- All complete and correct answers will be listed on a "Mathematical Puzzle List of Distinction" to be posted outside Wickersham 113 as well as on a "Mathematical Puzzle List of Distinction" web page.

Older puzzles may be found here.