What's in Convergence? - Contents of Volume 18 - 2021

Editors:  Amy Ackerberg-Hastings, Janet Heine Barnett

Associate Editors:  Paul Bialek, Eugene Boman, Maureen Carroll (through 1/31/21), Ximena Catepillan, Sloan Despeaux, Joel Haack, Toke Knudsen, Stacy Langton, Betty Mayfield, Michael Molinsky, Andrew Perry, Adrian Rice, Elyn Rykken (through 1/31/21), Amy Shell-Gellasch, Gary Stoudt (through 1/31/21), Erik R. Tou, Laura Turner

Founding Editors: Victor Katz, Frank Swetz


E. G. Ziegenbalg’s Danish Translation of Euclid’s Elements, by Toke Knudsen
Introduces the first (1744) translation into Danish of the classic geometry text, influences on its content that led to a distinctive pedagogical approach, and the notable family who owned the author’s copy. (posted 10/18/2021)

Algebra Tiles Explorations of al-Khwārizmī’s Equation Types, by Günhan Caglayan
Activities for visualizing al-Khwārizmī's algebraic solution methods using algebra tile manipulatives. (posted 10/04/2021)

Helping Ada Lovelace with her Homework: Classroom Exercises from a Victorian Calculus Course, by Adrian Rice
Highlights from Ada Lovelace's correspondence course on calculus with Augustus De Morgan that shed light on common confusions that still arise today. (posted 09/03/2021)

The Life of Sir Charles Scarburgh, by Michael Molinsky
Biography of Sir Charles Scarburgh (ca 1615–1694) and discussion of his impressive mathematical library and potential role in the production of a rare mathematical treasure: The English Euclide (1705). (posted 06/06/2021)

Mark Kac’s First Publication: A Translation of "O nowym sposobie rozwiązywania równań stopnia trzeciego," by David Derbes
English translation of Mark Kac's first publication on a new derivation of Cardano’s formula, written while he was still in high school, with a typescript of the original Polish article, a biographical synopsis of Kac, the tale of the rediscoveries of the paper, and suggestions for classroom discussions of the cubic. (posted 04/18/2021)

HOM SIGMAA 2021 Student Paper Contest Winner
Read the winning entry, “The Suan shu shu and the Nine Chapters on the Mathematical Art: A Comparison” by Megan Ferguson, from the 18th annual edition of this contest. (posted 04/17/2021)

Mathematical Mysteries of Rapa Nui with Classroom Activities, by Ximena Catepillán, Cynthia Huffman, and Scott Thuong
A trip to Rapa Nui, also known as Easter Island, provided opportunities to explore the elliptical shape of the foundations of dwellings known as hare paenga and to learn about calendrical glyphs in Rapanui writing. Four activities involving ellipses help instructors share this example of ethnomathematics with their students. (posted 04/05/2021)

Misterios Matemáticos de Rapa Nui con Actividades para el Aula de Clases, por Ximena Catepillán, Cynthia Huffman, y Scott Thuong; traducido por Ximena Catepillán con la ayuda de Samuel Navarro
Un viaje a Rapa Nui, también conocida como Isla de Pascua, brindó oportunidades para explorar la forma elíptica de los cimientos de las viviendas conocidas como hare paenga y para aprender sobre glifos calendáricos en la escritura rapanui. Cuatro actividades que involucran elipses ayudarán a los profesores a compartir este ejemplo de etnomatemática con sus estudiantes. (publicado 09/03/2021)

The Educational Times Database: Building an Online Database of Mathematics Questions and Solutions Published in a 19th-Century Journal, by Robert M. Manzo
An introduction to a new tool and its potential uses for researchers and educators, with an overview of the significance of the ET and its contributors in the history of mathematics, as well as the history of efforts to index the run of mathematical problems and solutions in the Educational Times and its sister publication Mathematical Questions. (posted 03/22/2021)

The Evolutionary Character of Mathematics, by Richard M. Davitt and Judy Grabiner
Richard Davitt’s classroom application of Judy Grabiner’s “use-discover-explore/develop-define” model for historical change in mathematics, along with commentary by Grabiner. (posted 02/20/2021)

Ongoing Series

Keys to Mathematical Treasure Chests
A series that offers examples of how online databases of mathematical objects can be mined to unlock the collections that they preserve for use in research and teaching.

Teaching and Learning the Trigonometric Functions through Their Origins, by Daniel E. Otero
A series of curricular units based on primary source texts for use in teaching and learning trigonometry.

A Series of Mini-projects from TRansforming Instruction in Undergraduate Mathematics via Primary Historical Sources
A collection of student-ready projects for use in teaching standard topics from across the undergraduate curriculum.

Math Origins, by Erik R. Tou
How were concepts, definitions, and theorems familiar to today's students of mathematics developed over time?

Mathematical Treasures

Mathematical Treasures, by Frank J. Swetz

Index to Mathematical Treasures Collection: Images of historical texts and objects from libraries, museums, and individuals around the world for use in your classroom!

Mathematical Treasures added during 2021: