*Editors:* Amy Ackerberg-Hastings, Daniel E. Otero

*Associate Editors:* Phil Blau, Eugene Boman, Ximena Catepillan, Abe Edwards, Toke Knudsen, Stacy Langton, Betty Mayfield, Adam Parker, Andrew Perry, Adrian Rice, Laura Turner

*Founding Editors:* Victor Katz, Frank Swetz

### Articles

Geometría Maya en la Sala de Clases, por John C. D. Diamantopoulos y Cynthia J. (Woodburn) Huffman; traducido por Ximena Catepillán con la ayuda de Samuel Navarro

Los autores explican cómo los Maya hicieron un uso extensivo de la geometría en la arquitectura y el arte, y presentan tres actividades estudiantiles basadas en la geometría maya. Traducido al español de un artículo de *Convergence* publicado en 2013, “Maya Geometry in the Classroom.” (posted 8/19/2024)

HOM SIGMAA 2024 Student Paper Contest Winners

Read the four winning papers from the 21st annual edition of this contest. (posted 6/17/2024)

### Ongoing Series

**Historical Notes for the Calculus Classroom**, by V. Frederick Rickey

A series of short articles on the history of calculus, developed through the author’s experiences with historical research and teaching and written for the use of instructors.

**Historically Speaking**, by Betty Mayfield

Selections from the short columns on historical mathematics that ran in NCTM’s *Mathematics Teacher* between 1953 and 1969, with new commentary placing the history and mathematics into context.

**Quotations in Context**, by Michael Molinsky

A series of columns that explores the origins and meanings of various quotations about mathematics and mathematicians.

**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.

**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, Nicholas A. 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 David 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 Nicholas A. 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
- How to Calculate \(\pi\): Buffon's Needle – A Mini-Primary Source Project on Geometric Probability for Calculus 2 Students, Pre-service Teachers and Others, by Dominic Klyve
- Solving Linear Higher Order Differential Equations with Euler and Johann Bernoulli: A Mini-Primary Source Project for Differential Equations Students, by Adam E. Parker
- Fourier’s Infinite Series Proof of the Irrationality of e: A Mini-Primary Source Project for Calculus 2 Students, by Kenneth M Monks
- Fermat’s Method for Finding Maxima and Minima: A Mini-Primary Source Project for Calculus 1 Students, by Kenneth M Monks
- The Closure Operation as the Foundation of Topology: A Mini-Primary Source Project for Topology Students, by Nicholas A. Scoville
- Beyond Riemann Sums: Fermat's Method of Integration – A Mini-Primary Source Project for First-Year Calculus Students, by Dominic Klyve
- Lagrange’s Work on Wilson’s Theorem: Three Mini-Primary Source Projects for Number Theory Students, by Carl Lienert
- Three Hundred Years of Helping Others: Maria Gaetana Agnesi on the Product Rule – A Mini-Primary Source Project for Calculus 1 Students, by Kenneth M Monks
- Solving First-Order Linear Differential Equations: Three Mini-Primary Source Projects for Differential Equations Students, by Adam E. Parker
- A Compact Introduction to a Generalized Extreme Value Theorem: A Mini-Primary Source Project for Topology Students, by Nicholas A. Scoville
- L’Hôpital’s Rule: A Mini-Primary Source Project for Calculus 1 Students, by Daniel E. Otero

### 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 2024:

- Nasīr al-dīn al-Ṭūsī’s
*Tadhkirah uṣūl handasah al-ḥisāb li-Uqlīdis* (Commentary on Euclid’s *Elements*, 1485, 13th-century original)
- Gaspar Lax’s
*Arithemetica speculativa* (1515)
- Gaspar Lax’s
*Proportiones* (1515)
- Johann Heinrich Alsted’s
*Methodus admirandorum mathematicorum: complectens novem libris matheseos universae** *(1613, 1623)
- Ismaël Boulliau’s
*Exercitationes geometricæ tres* (1647)
- Grégoire de Saint-Vincent’s
*Opus geometricum quadraturae circuli et sectionum coni. Decem libris comprehensum* (1647)
- Johann Jakob Heinlin’s
*Synopsis Mathematica* (1653)
- Ismaël Boulliau’s
*De lineis spiralibus: Demonstrationes novae* (1657)
- Christoph Nottnagel’s
*Synopsis mathematica: continens mathesin generalem, arithmeticam, geometricam, astronomiam, geographiam* (1657)
- Johann Placentinus’s
*Geotomia, sive Terrae sectio, exhibens praecipua & difficiliora problemata * (1657)
- Andreas Cellarius’s
*Harmonia **Macrocosmica**, **seu** Atlas Universalis Et Novus* (1661, 1660 original)
- Gaspar Schott’s
*Cursus Mathematicus sive absoluta omnium mathematicarum disciplinarum encyclopædia *(1661), contributed by Jacqueline M Dewar and Sarah J Greenwald
- Johann Jakob Heinlin’s
*Synopsis Mathematica Universalis* (1663, 1653 original)
- Ismaël Boulliau’s
*Opus novum ad arithmeticam infinitorum* (1682)
- Johann Jakob Heinlin’s
*Synopsis Mathematica Universalis* (1679, 1653 original)
- Antoine Thomas’s
*Synopsis Mathematica complectens varios tractatus *(1685)
- Robert Steell’s
*A Treatise of Conic Sections* (1723)
- Emmanuel Caranza’s
*Phisicae Particularis Cursus *(1730)
- Thomas Simpson’s
*Mathematical Dissertations on a Variety of Physical and Analytical Subjects* (1743)
*The Analyst: or, An Introduction to the Mathematics: Containing the Doctrine of Vulgar and Decimal Fractions* (1746)
- Thomas Simpson’s
*Trigonometry, Plane and Spherical; With the Construction and Application of Logarithms* (1748)
- Francis Walkingame’s
*The Tutor’s Assistant* (1752, 1751 original)
- Thomas Simpson’s
*Elements of Geometry* (1760, 1747 original)
- Thomas Simpson’s
*Select Exercises for Young Proficients in the Mathematicks* (edited by Charles Hutton, 1792, 1752 original)
- Thomas Simpson’s
*Trigonometry, Plane and Spherical; With the Construction and Application of Logarithms* (edited by E. L., 1810, 1748 original)
- Alexander Macfarlane’s
*Principles of the Algebra of Logic* (1879)
- Felix Klein’s
*Riemann'sche Flächen* (1892, 1894)
- Felix Klein’s
*Ueber die hypergeometrische Function* (1894)
- Carl David Tolmé Runge’s
*Graphical Methods* (1912)
- Alexander Macfarlane’s
*Lectures on Ten British Mathematicians of the Nineteenth Century* (1916)