This method using the area of regular polygons inscribed in circles to approximate a value for pi is similar to the method used by Archimedes using circumferences.
Students' Understanding of Counterexamples
Rebecca Vinsonhaler and Alison G. Lynch
This article focuses on students use and understanding of counterexamples and is part of a research project on the role of examples in proving. We share student interviews and offer suggestions for how teachers can support student reasoning and thinking and promote productive struggle by incorporating counterexamples into the classroom.