Variations on a Theorem of Varignon

Summary

We look at the well-known Varignon’s Parallelogram Theorem and a number of extensions and variations of the theorem to other polygons, linear circuits and polyhedra. The theorem provides a starting point for a fascinating mathematical investigation of interest to college geometry students and, perhaps especially, to prospective and current teachers of secondary and college mathematics.

Acknowledgments

The authors wish to thank the editor and reviewers whose insights and suggestions were extremely helpful in improving the exposition of this article.

Additional information

Notes on contributors

Sandy Norman

Sandy Norman ([email protected]) is a mathematics educator at the University of Texas at San Antonio. He received his BA in mathematics from the University of Virginia and masters and doctoral degrees at the University of Georgia. He is the Director of the San Antonio Virtual and Interactive Geometry project at the Institute of Texan Cultures and frequently teaches the graduate non-Euclidean geometry course.

Priya V. Prasad

Priya V. Prasad ([email protected]) is also a mathematics educator at the University of Texas at San Antonio. She graduated from Scripps College in 2006 with a BA in mathematics and religious studies, and with a PhD from the University of Arizona in 2014. She teaches geometry very often and is interested in how teachers build mathematical knowledge for teaching.