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

*Editor-Elect:* Danny Otero

*Associate Editors:* 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

HOM SIGMAA 2023 Student Paper Contest Winner

Read the winning paper from the 20th annual edition of this contest: “Nicole Oresme and the Revival of Medieval Mathematics” by Adin Charles Tinsley. (posted 05/23/2023)

Things Certain and Uncertain, by Michael P. Saclolo and Erik R. Tou

The story of a mathematical problem on the mechanics of hot air balloon flight that Euler was working on the very day of his death, presented in its historical context and accompanied by a classroom capsule with suggestions for how the mathematics of balloon flight can be used in a contemporary differential equations or physics course. (posted 5/22/2023)

Who? How? What? A Strategy for Using History to Teach Mathematics, by Patricia Wilson and Jennifer Chauvot

The authors review four benefits of using the history of mathematics in the classroom and suggest a strategy of asking *who* does mathematics, *how* mathematics is done, and *what* mathematics is in order to help students and instructors discover the human story of mathematics by beginning to explore its history. (posted 4/24/2023)

A Mysterious Copy of Lacroix’s *Traité Élémentaire de Calcul Différentiel et de Calcul Intégral*, by Adrian Rice

The author's recounting of an intriguing mystery surrounding his personal copy of the 4th edition of Lacroix's well-known textbook—a tale that involves Augustus De Morgan, James Joseph Sylvester, and the teaching of mathematics at University College London in its early days. (posted 3/27/2023)

Aiding the Teaching of Geometry and Affording Mathematical Recreation: Paper Folding in the Spirit of Sundara Rao of Madras, by Peggy Aldrich Kidwell

A history of paper folding in mathematics education that focuses on the background, publication, and reception of Sundara Rao’s 1893 *Geometrical Exercises in Paper Folding*. The article also describes several potential classroom activities for secondary and undergraduate students of geometry and preservice teachers. (posted 3/13/2023)

### 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.

**HoM Toolbox, or Historiography and Methodology for Mathematicians**

A series that guides readers through the basic principles and theoretical approaches for researching and writing the history of mathematics.

**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, 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
- 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

### 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 2023:

- Benedetto da Firenze’s
*Trattato d’abacho* (ca 1480)
- Peter Apian’s
*Cosmographia* (1539, 1524 original)
- Rafael Bombelli’s
*L'algebra parte maggiore dell’aritmetica divisa in tre libri* (1572)
- Niccolò Tartaglia’s
*Tutte l'opere d'arithmetica *(2 vol., 1592)
- Richard White’s
*Hemisphaerium dissectum opus geometricum* (1648)
- Bonaventura Cavalieri’s
*Lo specchio ustorio* (1650, 1632 original)
- Stefano degli Angeli’s
*Problemata geometrica sexaginta. Circa conos, sphaeras, superficies conicas, sphaericasque praecipue versantia* (1658)
- Stefano degli Angeli’s
*De superficie vngulae, et de quartis liliorum parabolicorum & cycloidalium tractatus duo geometrici* (1661)
- Christiaan Huygens’s
*Horologium Oscillatorium* (1673)
- Alessandro Marchetti’s
*Problemata sex à Leidensi quodam surveyor Christophoro Sadlerio* (1675)
- Vincenzo Viviani’s
*Formazione, e misvra di tutti i cieli* (1692)
- Vincenzo Viviani’s manuscript notes on his studies with Galileo (17th century)
- Gaspard Monge’s
*Applications de L’Analyse a la Géométrie* (1850, original 1807)
- Charles Babbage’s “Observations on the analogy which subsists between the calculus of functions and the other branches of analysis” (1817)
- Charles Babbage's
*Examples of the Solutions of Functional Equations* (1820)
- Charles Babbage’s “Observations on the notation employed in the calculus of functions” (1820)
- Charles Babbage’s “On the application of analysis to the discovery of local theorems and porisms” (1823)
- Charles Babbage’s “On the influence of signs in mathematical reasoning” (1826, read in 1821)
- Florence Nightingale’s
*Notes on Matters Affecting the Health, Efficiency, and Hospital Administration of the British Army* and contributions to *Mortality of the British Army* (both in 1858)
- James Clerk Maxwell’s
*Treatise on Electricity and Magnetism* (1873)
- Gaspard Monge’s
*Darstellende Geometrie* (1900, 1798 original)
- Srinivasa Ramanujan’s “Lost” Notebooks (1910s)
- David Eugene Smith and Louis Charles Karpinski’s
*The Hindu-Arabic Numerals* (1911)
- M. Raṅgācārya’s
*The Ganita-sāra-sangraha of Mahāvīrācārya*, with introduction by David Eugene Smith (1912, 9th-century original)
- David Eugene Smith’s second edition of Augustus De Morgan’s
*Budget of Paradoxes* (1915, 1872 original)
- David Eugene Smith’s
*History of Mathematics* (1923 and 1925)