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A Pair of Articles on the Parallelogram Theorem of Pierre Varignon

Pierre Varignon
(Source: Convergence Portrait Gallery)

Over the years, the journals of the National Council of Teachers of Mathematics (NCTM) have published numerous articles on the history of mathematics and its use in teaching. These journals include Teaching Children Mathematics, Mathematics Teaching in the Middle School, and Mathematics Teacher. Convergence founding co-editor Frank Swetz has arranged with NCTM to republish in Convergence (in pdf format) two articles from Mathematics Teacher annually. His picks for 2014 are two articles on the life and Parallelogram Theorem of French mathematician Pierre Varignon (1654-1722), including ideas for how the Parallelogram Theorem can be explored and extended in the classroom.

  • Pierre Varignon and the Parallelogram Theorem, by Peter N. Oliver. Mathematics Teacher, Vol. 94, No. 4 (April 2001), pp. 316-319. Reprinted with permission from Mathematics Teacher, © 2001 by the National Council of Teachers of Mathematics. All rights reserved.
  • Consequences of the Varignon Parallelogram Theorem, by Peter N. Oliver. Mathematics Teacher, Vol. 94, No. 5 (May 2001), pp. 406-408. Reprinted with permission from Mathematics Teacher, © 2001 by the National Council of Teachers of Mathematics. All rights reserved.

Parallelogram EFGH is formed by connecting the midpoints of the sides of quadrilateral ABCD. Is the quadrilateral formed by connecting midpoints of successive sides of any quadrilateral in fact a parallelogram?

In the second of his two articles, author Peter N. Oliver encouraged teachers to allow students to discover Varignon's Parallelogram Theorem for themselves. In 2014, he reiterated his advice, writing (via email from Honolulu, HI): 

Discovering the parallelogram for themselves could be a wonderful exploratory activity for second-semester geometry students.

About NCTM

The National Council of Teachers of Mathematics (NCTM) is the public voice of mathematics education, supporting teachers to ensure equitable mathematics learning of the highest quality for all students through vision, leadership, professional development, and research. It publishes five journals, one for every grade band, as well as one on the latest research and another for teacher educators. With 80,000 members and more than 200 Affiliates, NCTM is the world’s largest organization dedicated to improving mathematics education in prekindergarten through grade 12. For more information on NCTM membership, visit http://www.nctm.org/membership.

One more recommendation:

On the last page of the first of the two articles, you will see the end of another article with the intriguing title, “Geometric Approaches to Quadratic Equations from Other Times and Places.” This is another of our all-time favorite Mathematics Teacher articles, which we hope to obtain permission to reprint in the future. In the meantime, be sure to look it up for yourself; the full citation is as follows.

Patricia R. Allaire and Robert E. Bradley, “Geometric Approaches to Quadratic Equations from Other Times and Places,” Mathematics Teacher, Vol. 94, No. 4 (April 2001), pp. 308-313, 319.

"A Pair of Articles on the Parallelogram Theorem of Pierre Varignon," Loci (July 2014)

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