MAA Convergence Introduces Interactivity to Mathematics History

MAA Convergence is both an online journal on the history of mathematics and its use in teaching and an ever-expanding collection of online resources to help its readers teach mathematics using its history. Founded in 2004 by well-known mathematics historians and educators Victor Katz and Frank Swetz, Convergence brings you a variety of interesting articles and teaching tools. It is freely available from the Mathematical Association of America (MAA) website: http://www.maa.org/press/periodicals/convergence

We highlight here some of our newest articles and resources for use in your classroom. Many of them use interactive features to help students understand and explore historical mathematical ideas.

In “Ancient Indian Rope Geometry in the Classroom,” Cynthia Huffman and Scott Thuong offer information, activities, and applets to help you and your students explore the geometry of altar construction in ancient India. In the photograph, boys work on a model of the bird-shaped fire altar in an Agnicayana ritual in Panjal, Kerala, India in 2011. (Photo courtesy of Professor Michio Yano.)

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In “Geometrical Representation of Arithmetic Series,” Gautami Bhowmik explores a geometric tradition in Sanskrit arithmetic texts from Medieval India and shares problems from these texts for your students.

“Historical Activities for the Calculus Classroom,” by Gabriela Sanchis, presents curve-sketching, tangent lines, and optimization in the context of historical problems, and is illustrated by 24 interactive applets and 10 animations.

In “Descartes’ Method for Constructing Roots of Polynomials with ‘Simple’ Curves,” Gary Rubinstein explains and derives Descartes’ methods from his 1637 Geometry and illustrates them using interactive applets. The diagram shows a step in the construction of roots of sixth degree polynomials using a ‘Cartesian parabola’ and circles (from GeoGebra applet by Gary Rubinstein).

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In “Pythagorean Cuts,” Martin Bonsangue and Harris Shultz answer the question ‘Can Euclid’s proof of the Pythagorean Theorem be adapted to shapes other than squares?’ and encourage you to pose it to your students.

“Some Original Sources for Modern Tales of Thales,” by Michael Molinsky, features earliest known sources for stories about Thales, and applets illustrating methods attributed to him. The diagram shows how Thales might have measured the distance from ship to shore (from GeoGebra applet by Michael Molinsky).

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“A GeoGebra Rendition of One of Omar Khayyam’s Solutions for a Cubic Equation,” by Deborah Kent and Milan Sherman, explains and illustrates how the 11th century Persian mathematician, philosopher, and poet geometrically determined a positive real solution to a cubic equation.

“Edmund Halley, 1740” is an historical poem in which Halley reflects on his role in publishing Newton’s Principia, by award-winning Oxford poet Andrew Wynn Owen.

“D’Alembert, Lagrange, and Reduction of Order,” by Sarah Cummings and Adam Parker, offers two historical approaches, one familiar and one unfamiliar, to enrich your differential equations course.

In “Euler and the Bernoullis: Learning by Teaching,” author Paul Bedard reflects on lessons he has learned about mathematics teaching and learning from these great mathematicians.

In “Can You Really Derive Conic Formulae from a Cone?” Gary Stoudt uses 17 interactive applets to explain how attempts to double the cube led ancient Greek mathematicians to discover and develop the conic sections.

Finally our “Index to Mathematical Treasures” includes hundreds of images for use in your classroom, including photographs of “The Cambodian (Khmer) Zero” (of 683 CE) by Amir and Debra Aczel.

See all of these articles and more at MAA Convergence:

http://www.maa.org/press/periodicals/convergence

Join us at the Convergence of mathematics, history, and teaching!

Janet Beery

Editor, MAA Convergence

University of Redlands

(USA)

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