A Perfect Square Discovers Pi

Pi is defined as the ratio of the circumference of a circle, to its diameter. It follows (how?) that the same constant pi is also the number of r x r squares that have the same total area as a circle of radius r (and so the area of a circle is given as (pi) multiplied by r^2).
In this 5 minute video, young Squeaky the Square discovers pi in his own uniquely square way! Please enjoy!

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Dan McQuillan, Charles A. Dana Professor of Mathematics,
Department of Mathematics,
Norwich University,
Northfield, VT 05663,
802 485-2323,
dmcquill [at] norwich.edu.

There is a menu just under the picture of Norwich University (The options are: Home, Research, Publications, About, Selected Preprints, Talks on Video, and Poem). Please explore these pages of this site by clicking on the menu tabs.

If you click on “daniel-mcquillan” in small print, just under the title of any post, then you will see all posts in an abbreviated archive format. Alternatively, there are links to recent posts on the right side of this page.

In addition, several “blogroll” links are on the upper right side of this page, including links to certain journal papers.

Mathematics is a human activity; as such it is always changing and always exciting. It has a rich history and strong personalities. It is certainly a subject where we continuously learn more by re-examining what was done in the past. We are often looking for another perspective to deepen our understanding. I sincerely hope that you enjoy this article, partly on the Witt Cancellation Theorem, and partly a survey article, but also a tribute to many great mathematical personalities responsible for the birth of the algebraic theory of quadratic forms. We thank and honor a few of the founders, including Ernst Witt, Emmy Noether, and Leonard Dickson. We also celebrate the 75th birthday of a pioneering paper of Witt with a brief overview of recent spectacular work which is still building on his original creation of the the algebraic theory of quadratic forms.

A few preprints, including the slides for my talk, “Vertex-magic Graphs,” (given during the spring meeting of the Northeastern section of the Mathematical Association of America on June 11, 2011), have¬†been placed on the selected preprints page.

Click here for updates on our top performances in the Putnam competition!

Please check out the rest of the site and feel free to provide comment for the posts.

About me, Research, Publications

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