Stage: 5 Challenge Level: 
A square of side length 1 has a circle of radius 1 drawn from each of its corners, as in the following diagram. The circles intersect inside the square at four points, to create the shaded region.
How large is the largest square that can be completely contained within the shaded region? Is this a good estimate of the actual area? Can you give a bound on the size of the error?
What is the exact area of the central shaded region?
Click here for a poster of this problem.
Mathematical reasoning & proof. Discussion. Maths in STEM. Cartesian equations of circles. Stage 5 - Core Mapping. Calculus generally. Integration. Weekly Challenge. Individual. Integration by substitution.
Published June 2009.
Copyright © 2007. University of Cambridge. All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project, which also includes the Plus and Motivate sites.
email: nrich@damtp.cam.ac.uk