MAA Convergence: Mathematics History With Online Interactivity

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, the Mathematical Association of America’s Convergence brings you a variety of interesting articles and teaching tools.

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.

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In “Exploring Liu Hui’s Cube Puzzle: From Paper Folding to 3-D Design,” author Lingguo Bu offers history, classroom activities, and interactive applets to help you and your students explore Liu Hui’s 3rd century dissection of the cube into three pieces with volumes 1/2, 1/3, and 1/6 of the volume of the cube. The three puzzle pieces are shown above and below. The pieces in the image below were made using a 3-D printer.

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For a different kind of puzzle, try “Mathematicians from A to Z,” a New York Times-style crossword puzzle created by mathematics instructor Sid Kolpas and a crossword puzzle creator Stu Ockman.

The article, “Misseri-Calendar: A Calendar Embedded in Icelandic Nature, Society, and Culture,” by Kristín Bjarnadóttir, reviews the calendar’s long history from Viking times to the present, and offers animations and ideas for your classroom.

In “A Translation of Evangelista Torricelli’s ‘The Quadrature of the Parabola, solved by many methods through the new geometry of indivisibles,’” authors Andrew Leahy and Kasandra Sullivan provide plenty of history and helpful diagrams along with their translation.

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In “A Series of Mini-projects from TRansforming Instruction in Undergraduate Mathematics via Primary Historical Sources” the TRIUMPHS team introduces the first of a collection of mini-Primary Source Projects (mini-PSPs), “The Derivatives of the Sine and Cosine Functions” (by Dominic Klyve), a classroom assignment in which Calculus I students learn how Leonhard Euler (1707-1783) obtained these derivatives via differentials. Above, students work on a Primary Source Project under the supervision of Janet Barnett at a TRIUMPHS Site Tester Workshop in Denver, Colorado, in September of 2016.

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In “Illustrating The Nine Chapters on the Mathematical Art: Their Use in a College Mathematics History Classroom,” author Joel Haack shares how he used his experiences on an MAA Mathematical Study Tour to China to enrich his teaching. The photo above is of a statue in the National Museum of China of a civil servant from the Sui Dynasty (581-618), an intended user of the Nine Chapters.

“Moses ibn Tibbon’s Hebrew Translation of al-Hassar’s Kitab al Bayan,” by Jeremy I. Pfeffer (Hebrew University of Jerusalem) features the arithmetic of fractions as you’ve (possibly) never seen it before!

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See fractions in the context of problem-solving using the method of double false position in the Arabic manuscript Kitab al-nuzah in “Mathematical Treasure: The Method of Scales in ibn al-Ha’im’s Book of Delights,” by Randy Schwartz and Frank Swetz. Above: This diagram is used in this and other manuscripts to illustrate and carry out the “method of scales.”

In “Mathematical Treasures at the Linda Hall Library,” author Cynthia Huffman highlights the mathematics collections available at this rare book library in Kansas City, Missouri. See images of mathematics books by Euclid, Pacioli, Cardano, Torricelli, Maria Agnesi, and Emilie du Chatelet.

Our “Index to Mathematical Treasures” includes hundreds of images for use in your classroom from dozens of libraries and sources.

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, California

USA

 

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