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Intersections of a Circle and a Square: An Investigation

Dan Canada, Stephen Blair 

January 2007, Volume 100, Issue 5, Page 324

Abstract:
The investigation of how a circle and square lying in the same plane could intersect each other is an excellent example of geometric problem-solving. This paper explores three facets of the investigation: (1) finding out how many points of intersection are possible, (2) classifying the different ways of intersection, and (3) determining which ways are constructible, and how. Altogether, the investigation offers students and teachers alike a venue for exploring a rich task in geometry. Includes student work.

Keywords:
Article
Computers
Teacher in Training / Preservice Teacher
Grades 9-12
Geometry & Measurement
Problems
Problem Solving / Problem Posing
Student Work
Reasoning and Proof