Park City Mathematics Institute Investigating Geometry Project Abstract Drafts of Project Files (password required)

Going in Circles: Exploring Perimeter and Area through Dilating Cyclic Polygon

Jennifer Outzs*, Jennifer Saint-Preux, Carol Spice

Students explore how dilating a circle affects the perimeter and area of an inscribed or cyclic polygon. The activity of inscribing a polygon, dilating it and then exploring how the dilation affects the perimeter and area is appropriate for both middle and high school students. This concept can be extended to explore generalized rules, proofs, and conjectures created by the students.

 

Under Construction: Exploring Perimeter and Area through Dilating Cyclic Polygon

Assegid Derseh, Emily Gorman, Adnan Rubai, Michael Simone*

The project was born out of our interest in integrating constructions into our curricula in a non-superficial way, and investigating the connections to the wider world of geometry. Using only a compass and straightedge, we want students to be able to create polygons and solve problems with either a purely mathematical or a "real world" context. We want to take constructions out of isolation and relate them to properties of polygons, congruent triangles, square roots (among others), area, locus and proof.

 

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This material is based upon work supported by the National Science Foundation under Grant No. 0314808.
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.