*Editors:* Amy Ackerberg-Hastings, Janet Heine Barnett

*Associate Editors:* Paul Bialek (through 1/31/22), Eugene Boman, Ximena Catepillan, Sloan Despeaux (through 1/31/22), Joel Haack, Toke Knudsen, Stacy Langton, Betty Mayfield, Michael Molinsky, Adam Parker, Andrew Perry, Adrian Rice, Amy Shell-Gellasch, Erik R. Tou, Laura Turner

*Founding Editors:* Victor Katz, Frank Swetz

### Articles

An Ancient Egyptian Mathematical Photo Album – Hieroglyph Numerals and More by Cynthia J. Huffman

Photographs of ancient Egyptian hieroglyphs in authentic contexts that instructors can use when teaching numeration systems. (posted 4/9/2022)

Kepler and the Rhombic Dodecahedron by Roberto Cardil

Resources for sharing Kepler's fascinating studies of the rhombic dodecahedron with students. (posted 3/19/2022)

The High School Mathematics Curriculum—What Can We Learn from History? by Robert Reys and Barbara Reys

The authors review several of the major programs for reform in American mathematics education that appeared between 1894 and 2010 and conclude that, while calls for change have been constant, the full implementation of different approaches is much more difficult to achieve. (posted 3/05/2022)

Reflections on Chinese Numeration Systems, by Frank J. Swetz

Recommends ancient Chinese rod numerals to the instructors of preservice elementary teachers as an alternative place-value numeration system for helping students understand the structures and operations of arithmetic. Includes historical descriptions and classroom suggestions. (posted 2/20/2022)

Building a Book: HathiTrust, Ancestry.com, Serendipity, and Lifetime Interests, by David Lindsay Roberts

Reveals how personal knowledge, changes in historical research methods, and unexpected discoveries came together in the preparation of a book on the history of American mathematics, and suggests how the lessons learned could be incorporated into history of mathematics and other courses. (posted 1/22/2022)

### 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.

- 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 1, 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 2 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 2 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
- Babylonian Numeration: A Mini-Primary Source Project for Pre-service Teachers and Other Students, by Dominic Klyve
- Wronskians and Linear Independence: A Theorem Misunderstood by Many – A Mini-Primary Source Project for Students of Differential Equations, Linear Algebra and Others, by Adam E. Parker
- Bhāskara’s Approximation to and Mādhava’s Series for Sine: A Mini-Primary Source Project for Calculus 2 Students, by Kenneth M Monks
- The Logarithm of -1: A Mini-Primary Source Project for Complex Variables Students, by Dominic Klyve
- Gaussian Guesswork: Three Mini-Primary Source Projects for Calculus 2 Students, by Janet Heine Barnett
- Fourier’s Heat Equation and the Birth of Modern Climate Science: A Mini-Primary Source Project for Differential Equations and Multivariable Calculus Students, by Kenneth M Monks

### 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 2022: