*Editors:* Amy Ackerberg-Hastings, Janet Barnett

*Associate Editors:* Paul Bialek, Eugene Boman, Maureen Carroll, Ximena Catepillan, Lawrence D'Antonio (through 1/31/20), Sloan Despeaux, Toke Knudsen, Michael Molinsky, Adrian Rice, Elyn Rykken, Randy Schwartz (through 1/31/20), Amy Shell-Gellasch, Jody Sorensen (through 1/31/20), Gary Stoudt, Erik R. Tou, Laura Turner

*Founding Editors:* Victor Katz, Frank Swetz

### Articles

The French Connection: Borda, Condorcet and the Mathematics of Voting Theory, by Janet Heine Barnett

An overview of two eighteenth-century texts on voting theory with biographical and historical notes about their authors, Jean-Charles de Borda and Nicolas Condorcet, accompanied by a classroom-ready project based on their original writings suitable for use with Liberal Arts and high school students. (posted 09/22/2020)

Apportionment: What's Your Fair Share – An Activity for Liberal Arts and High School Students, by Jeff Suzuki

A self-contained project suitable for individual or group work, inside or outside the classroom, that uses US Census data from 1790 to guide students through an exploration of what it means for each state to get its fair share of congresspersons, and of how different methods of apportionment might have altered the course of American history. (posted 09/08/2020)

Pathways from the Past: Classroom-Ready Materials for Using History to Teach Mathematics, by Bill Berlinghoff and Fernando Gouvêa

Reproducible student activity sheets developed by the authors of the well-regarded textbook, *Math through the Ages*, and especially suitable for practicing and pre-service teachers of secondary mathematics and those involved in teacher training. (posted 06/07/2020)

HOM SIGMAA 2020 Student Paper Contest Winner

Read the winning entry, “Did Archimedes Do Calculus?” by Jeffrey Powers, from the 17th annual edition of this contest. (posted 05/11/2020)

Word Histories: Melding Mathematics and Meanings, by Rheta N. Rubenstein and Randy K. Schwartz

Etymologies for common mathematical terms—from subjects such as algebra, geometry, functions and discrete mathematics—can be used by instructors to enrich student learning. (posted 04/20/2020)

Mabel Sykes: A Life Untold and an Architectural Geometry Book Rediscovered, by Maureen T. Carroll and Elyn Rykken

Biography of a little-known high-school mathematics teacher and discussion of her publications, particularly the lavishly-illustrated 1912 *A Source Book of Problems for Geometry Based upon Industrial Design and Architectural Ornament*. The description of *Source Book* includes diagrams and animations. (posted 2/24/2020)

Why History of Mathematics? by Glen Van Brummelen

Justifications for using history to teach mathematics that were prepared to help secondary teachers in British Columbia understand how to approach a new 11th-grade course but which are widely applicable. (posted 1/27/2020)

A Mathematical History Tour: Reflections on a Study Abroad Program, by R. Abraham Edwards and Marie Savoie

A unique study-abroad course combining the history of mathematics and travel. (posted 1/13/2020)

### Ongoing Series

**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.

- Series Introduction, by Janet Barnett, Kathy Clark, Dominic Klyve, Jerry Lodder, Daniel E. Otero, Nick Scoville, and Diana White
- The Derivatives of the Sine and Cosine Functions: A Mini-Primary Source Project for Calculus I, by Dominic Klyve
- Why be so Critical? Nineteenth Century Mathematics and the Origins of Analysis: A Mini-Primary Source Project for Introductory Analysis Students, by Janet Heine Barnett
- Connecting Connectedness: A Mini-Primary Source Project for Topology Students, by Nicholas A. Scoville
- Generating Pythagorean Triples: A Mini-Primary Source Project for Mathematics Majors, Elementary Teachers and Others, by Janet Heine Barnett
- Euler's Rediscovery of
*e:* A Mini-Primary Source Project for Introductory Analysis Students, by Dave Ruch
- How to Calculate \(\pi\): Machin's Inverse Tangents, A Mini-Primary Source Project for Calculus II Students, by Dominic Klyve
- Henri Lebesgue and the Development of the Integral Concept: A Mini-Primary Source Project for Undergraduate Analysis Students, by Janet Heine Barnett
- Seeing and Understanding Data: A Mini-Primary Source Project for Students of Statistics, by Charlotte Bolch and Beverly Woods
- The Origin of the Prime Number Theorem: A Primary Source Project for Number Theory Students, by Dominic Klyve
- The Cantor Set Before Cantor: A Mini-Primary Source Project for Analysis and Topology Students, by Nicholas A. Scoville
- Euler’s Calculation of the Sum of the Reciprocals of the Squares: A Mini-Primary Source Project for Calculus II Students, by Kenneth M Monks
- Completing the Square: From the Roots of Algebra, A Mini-Primary Source Project for Students of Algebra and Their Teachers, by Daniel E. Otero
- Regression to the Mean: A Mini-Primary Source Project for Statistics Students, by Dominic Klyve
- Investigations Into d'Alembert's Definition of Limit: A Mini-Primary Source Project for Students of Real Analysis and Calculus 2, by David Ruch
- Braess’ Paradox in City Planning: A Mini-Primary Source Project for Multivariable Calculus Students, by Kenneth M Monks
- Topology from Analysis: A Mini-Primary Source Project for Topology Students, by Nick Scoville

**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 at the Linda Hall Library, by Cynthia J. Huffman

Mathematical Treasures from the Linda Hall Library added during 2020:

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 2020:

- Works of Boethius (10th-12th centuries)
- Mathematics of Gerbert of Aurillac (12th-13th centuries)
- Johannes de Sacrobosco's
*Algorismus* (13th century)
- Manuscript illustrations of tools of measurement (15th century)
- Juan de Ortega's
*Suma de arithmetica: ordinate* (1515, original 1512)
*Algorithmus Demonstratus* (1534)
- Oronce Fine's
*Arithmetica practica* (1544), contributed by Sid Kolpas
- Piero Borghi's
* Libro de Abacho* (1550, original 1484)
*Arithmeticae practicae* of Gemma Frisius (1556, original 1540)
- Adriaan Metius's
*Manuale arithmetice et geometrie practice* (1634)
- Bonaventura Cavalieri's
*Trigonometria Plana et Sphaerica, Linearis, & Logarithmica *(1643)
- Jean François's
*Traité de la Quantitée* (1655)
- Jean François's
*L’Arithmétique et la Géométrie Pratique* (1657)
- Giovanni Alfonso Borelli's
*Euclide rinnovato* (1663)
- Lorenzo Forestani's
*Pratica d'arithmetica e geometria* (1682, original 1603)
- Jean Boulenger's
*La Geometrie Pratique *(1691, original 1624)
- Ignatius Pardies's
*Short but Plain Elements of* *Geometry and Plain Trigonometry *(1701)
- Jacques Ozanam's
*La Trigonometrie Rectiligne et Spherique* (1741)
- José Fernandes Pinto Alpoim's
*Exame de Artilheiros* (1744)
- James Dodson's
*The Mathematical Repository*, 3 vol. (1748, 1753, 1755)
- Edward Waring's
*Proprietates algebraicarum curvarum* (1772)
- Colin Maclaurin's
*Treatise of Algebra *(1796, original 1748)
- Étienne Bézout's
*Cours de Mathématiques *(1815, original 1770–1782)
- Condorcet's books on Probability (1785, 1805)
- William Frend's Algebra and Arithmetic texts (1796, 1805 respectively)
- French translation of Gauss's
*Disquistiones Arithmeticae* (1807, original 1801)
- August Leopold Crelle's
*Journal für die reine und angewandte Mathematik* (1826–present)
- George Peacock's
*Treatise on Algebra* (1830)
- Farkas Bolyai's
*Tentamen juventutem studiosam* (1832)
- George Boole's
*A Treatise on **Differential Equations *(1865, original 1859)
- Jules Hoüel's
*Eléments de la théorie des quaternions* (1874)
- William Clifford's
*Mathematical Fragments* (1881)
- Oliver Heaviside's
*Electromagnetic Theory* (1893–1912)
- Walt Disney's
*Donald in Mathmagic Land *(1959), contributed by Sid Kolpas