Posts Tagged ‘Convergence’

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.


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.


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.


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.


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!


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:


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


Janet Beery

Editor, MAA Convergence

University of Redlands, California



Mathematical Association of America’s Convergence is undergoing many changes (as part of a website conversion). Please visit the journal’s homepage:

Below are several short abstracts of recently published articles.


 Diamantopoulos, John; and Woodburn, Cynthia. Maya Geometry in the Classroom. Loci: Convergence (August 2013), 5 pp., electronic only. The authors show how classic Maya people may have used knotted ropes to form desired geometric shapes in art and architecture.


Branson, William B. Solving the Cubic with Cardano. Loci: Convergence (September 2013), 8 pp., electronic only. The author shows how, in order to solve the cubic, Cardano relied on both classical Greek geometric and abbaco traditions, and he illustrates Cardano’s geometric thinking with modern manipulatives.


18th Century

Wardhaugh, Benjamin. Learning Geometry in Georgian England. Loci: Convergence (August 2012), 6 pp., electronic only. A comparison of the geometry found in two 18th century copybooks written with two different purposes, mental acumen and practical application. DOI:10.4169/loci003930

18th and 19th Centuries

Wessman-Enzinger, Nicole M. An Investigation of Subtraction Algorithms from the 18th and 19th Centuries. Loci: Convergence (January 2014), 9 pp., electronic only.  This survey of subtraction algorithms used in North America includes both handwritten “cyphering books” and printed arithmetic books.

19th Century

Del Latto, Anthony J.; and Petrilli, Salvatore J., Jr. Robert Murphy: Mathematician and Physicist. Loci: Convergence (September 2013), 8 pp., electronic only. The authors argue that Murphy (1806-1843) showed “true genius” during his very short life, and they provide a transcription of Murphy’s first published work in 1824.

20th Century

Beery, Janet; and Mead, Carol. Who’s That Mathematician? Images from the Paul R. Halmos Photograph Collection. Loci: Convergence (January 2012 – March 2013), 60 pp., electronic only. For each of 343 photographs taken by functional analyst and mathematical expositor Halmos from 1950 to 1990, the authors identify the subjects and provide biographical information about them. DOI:10.4169/loci003801

Meyer, Walter. External Influences on U.S. Undergraduate Mathematics Curricula: 1950-2000. Loci: Convergence (August 2013), 8 pp., electronic only. An examination of the influence of forces outside of mathematics on such curricular changes as increased emphasis on applications and modeling, introduction of discrete mathematics courses, and calculus reform.


Janet Beery,

Editor, MAA Convergence

 Professor of Mathematics

Department of Mathematics and Computer Science

University of Redlands

1200 E. Colton Ave.

Redlands, CA 92373