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