Visit the Convergence of Mathematics, History, and Teaching!

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. We highlight here some of our newest articles and resources for use in your classroom.
As a web-based publication, Convergence aims to take advantage of new technologies in order to present, explore, and better understand what are often very old ideas. The articles and resources featured here all exemplify this combination of old and new.

(1) “Euclid21: Euclid’s Elements for the 21st Century” introduces a dynamic, interactive version of Euclid’s classic circa 300 BCE geometry text organized via its logical structure.


Figure 1. Euclid’s first three uses of his Parallel Postulate, as illustrated in Euclid21 (Image from Euclid21 computer application created by Eugene Boman and his student team)
(2) “Oliver Byrne: The Matisse of Mathematics” offers both the most complete biography of Byrne to date and ideas for using Byrne’s colorful Euclid’s Elements (1847) in the classroom.


Figure 2. Byrne’s illustration of Euclid’s “windmill” proof of the Pythagorean Theorem. Byrne’s color-coded Euclid was a marvel of Victorian printing and of Pestalozzian pedagogy. (Photo by author Sid Kolpas of his own copy of the book)

(3) “Bridging the Gap Between Theory and Practice: Astronomical Instruments” shows how your students can design and build armillary spheres, astrolabes, quadrants, sextants, and sundials using such modern technology as 3D printers.


Figure 3. Student-built sundial from Toke Knudsen’s Ancient Mathematical Astronomy course at SUNY Oneonta (photo by T. Knudsen). See “Bridging the Gap Between Theory and Practice: Astronomical Instruments.”
(4) “Problems for Journey Through Genius: The Great Theorems of Mathematics” celebrates the popular book’s 25th year in print with downloadable problem sets for each chapter by author William Dunham himself.


Figure 4. Students can explain how Archimedes wrote the area of an ellipse in terms of the area of a circumscribing circle. (Image created by Janine Stilt)


(5) In “Pantas’ Cabinet of Mathematical Wonders: Images and the History of Mathematics,” Convergence’s chief treasure-hunter Frank Swetz showcases Convergence’s “Mathematical Treasures,” an ever-growing collection of hundreds of images of historical texts, manuscripts, and objects for classroom use. Search or browse “A Collection of Mathematical Treasures – Index.”


Figure 5a. A simple but compelling application of the Pythagorean Theorem from Robert Recorde’s Pathway to Knowledge (1551)


Figure 5b. Caption: Book VI of Euclid’s Elements (originally composed circa 300 BCE) begins with a definition of similar rectilinear figures. This copy of Euclid’s Elements was handwritten on vellum around 1294 CE. (Image courtesy of Columbia University Libraries)

(6) “Online Museum Collections in the Mathematics Classroom” introduces 27 mathematical object collections from the Smithsonian Institution’s National Museum of American History and offers suggestions for using them with students of all ages.


Figure 6. Grunow’s circa 1860 spherometer (Photo courtesy of Smithsonian Institution)

(7) “Jan Hudde’s Second Letter: On Maxima and Minima” contains a translation of the letter and explanation of Hudde’s pre-calculus optimization methods, including an early quotient rule.


Figure 7. Diagram added by Frans van Schooten when he published Hudde’s “second letter” in 1659. (Image courtesy of ETH-Bibliothek, Zürich, Switzerland)

(8) “Alan Turing in America” focuses on the important projects in logic and computing Turing worked on during two visits to the U.S.


Figure 8. This photo of a young Alan Turing is believed to be from 1936-38 when he was at Princeton University. (Photo from Convergence Portrait Gallery)

See all of these articles and more at MAA Convergence:

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

Janet Beery (USA)
Editor, MAA Convergence
University of Redlands


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