Given a circle, inscribe a square and circumscribe a square about the circle.
What is the ratio of the area of the inscribed square to the area of the circle
to the area of the circumscribed square?
Solution to the Problem:
Here is another way to see the ratio of the smaller square to the larger square.
Rotate and observe the little triangles. Four of them make up the smaller
square and eight of them make up the larger square. I have shaded two of them in red
in the diagram below.
Correctly solved by:
| 1. Walt Arrison | Philadelphia, Pennsylvania |
| 2. Trey Mason | Winchester, Virginia |
| 3. David & Judy Dixon | Bennettsville, South Carolina |
| 4. Chris McCormick | Virginia Tech, Blacksburg, Virginia |
| 5. James Alarie | University of Michigan -- Flint, Flint, Michigan |
| 6. Suzanne Timmons | Rocky Point, North Carolina |
| 7. Daniel Surber | Winchester, Virginia |
| 8. Kaveh Malekanian | Toronto, Ontario, Canada |
| 9. Erik Hultgren | Tullängskolan, Örebro, Sweden |
| 10. Sharina Broughton | Old Dominion University, Newport News, Virginia |
| 11. Ann Norman | Columbus, Georgia |
| 12. Dave Smith | Toledo, Ohio |
| 13. Emily Auerbach | Columbus, Georgia |
| 14. Jeffrey Gaither | Winchester, Virginia |
| 15. Misty Carlisle | Winchester, Virginia |
| 16. Jason LaRusso | Winchester, Virginia |
| 17. Keith Mealy | Cincinnati, Ohio |
| 18. Angelo Leone | Middletown, Connecticut |
| 19. Sarah Watterson | Middletown, Connecticut |
| 20. Jonas Sutinen | Tullängskolan, Örebro, Sweden |
| 21. Matt McMurtry | Arlington, Virginia |