The Theodorus Variation

Authors

  • Ewan Brinkman Simon Fraser University
  • Robert Corless Western University
  • Veselin Jungic Simon Fraser University

DOI:

https://doi.org/10.5206/mt.v1i2.14500

Keywords:

Spiral, root snail, Theodorus, evalf/Sum, Levin's u-transform, infinite product

Abstract

The Spiral of Theodorus, also known as the "root snail" from its connection with square roots, can be constructed by hand from triangles made with from paper with scissors, ruler, and protractor.  See the Video Abstract.  Once the triangles are made, two different but similar spirals can be made.  This paper proves some things about the second spiral; in particular that the open curve generated by the inner vertices monotonically approaches a circle, and that the vertices are ultimately equidistributed around that inner circle.

  

Author Biographies

Ewan Brinkman, Simon Fraser University

Ewan Brinkman is a first year student in Computing Science at Simon Fraser University, and is interested in applying computing and math to interesting challenges.

Robert Corless, Western University

Editor-in-Chief of Maple Transactions

Veselin Jungic, Simon Fraser University

Veselin Jungic is a Teaching Professor at the Department of Mathematics, Simon Fraser University, a Fellow of the Canadian Mathematical Society, and a Canadian 3M National Teaching Fellow. Most of his research is in Ramsey theory and the field of mathematics education and outreach.

The spiral of Theodorus and its reversal on the same graph. It looks like a wire-frame nautilus (the mollusc) with a blue outline and red spokes and a central "eye" at the unit circle

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Published

2021-11-29

Issue

Vol. 1 No. 2 (2021): Second Issue

Section

Student Corner

License

Copyright (c) 2021 Ewan Brinkman, Robert Corless, Veselin Jungic

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.