Problem of the Unit Circle

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.

Rules:

  1. Answers must be written neatly on 8.5 by 11 inch paper.
  2. Answers must be submitted to Dr. Buchanan either at his office (Wickersham 113) or placed in his department mailbox by the department secretary.
  3. The contest will open on July 20, 1998.
  4. The first complete and correct answer will be awarded the sum of $5.00 (five US dollars).
  5. 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.

Last updated: December 30, 2005