Article Series in Convergence

In addition to stand-alone articles, Convergence encourages submissions for series providing information, resources, and classroom-ready materials suitable for teaching mathematics through its history. Series that have appeared in Convergence are listed below:

Reprints from NCTM’s Mathematics Teacher

• Patricia R. Allaire and Robert E. Bradley, “Geometric Approaches to Quadratic Equations from Other Times and Places,” Mathematics Teacher, Vol. 94, No. 4 (April 2001), pp. 308–313, 319.
• David M. Bressoud, "Historical Reflections on Teaching Trigonometry," Mathematics Teacher, Vol. 104, No. 2 (September 2010), pp. 106–112, plus three supplementary sections, "Hipparchus," "Euclid," and "Ptolemy."
• Richard M. Davitt, “The Evolutionary Character of Mathematics,” Mathematics Teacher, Vol. 93, No. 8 (November 2000), pp. 692–694.
• Keith Devlin, "The Pascal-Fermat Correspondence: How Mathematics Is Really Done," Mathematics Teacher, Vol. 103, No. 8 (April 2010), pp. 578–582.
• Jennifer Horn, Amy Zamierowski and Rita Barger, “Correspondence from Mathematicians," Mathematics Teacher, Vol. 93, No. 8 (November 2000), pp. 688–691.
• Seán P. Madden, Jocelyne M. Comstock, and James P. Downing, “Poles, Parking Lots, & Mount Piton: Classroom Activities that Combine Astronomy, History, and Mathematics,” Mathematics Teacher, Vol. 100, No. 2 (September 2006), pp. 94–99.
• Peter N. Oliver, “Pierre Varignon and the Parallelogram Theorem,” Mathematics Teacher, Vol. 94, No. 4 (April 2001), pp. 316–319.
• Peter N. Oliver, “Consequences of the Varignon Parallelogram Theorem,” Mathematics Teacher, Vol. 94, No. 5 (May 2001), pp. 406–408.
• Rheta N. Rubenstein and Randy K. Schwartz, “Word Histories: Melding Mathematics and Meanings,” The Mathematics Teacher, Vol. 93, No. 8 (November 2000), pp. 664–669.
• Shai Simonson, “The Mathematics of Levi ben Gershon,” Mathematics Teacher, Vol. 93, No. 8 (November 2000), pp. 659–663.
• Frank Swetz, “The ‘Piling Up of Squares’ in Ancient China,” Mathematics Teacher, Vol. 73, No. 1 (January 1977), pp. 72–79.

Math Origins

Erik R. Tou explores how concepts, definitions, and theorems familiar to today's students of mathematics were developed over time.

• Math Origins: The Totient Function
• Math Origins: Orders of Growth
• Math Origins: Eigenvectors and Eigenvalues
• Math Origins: The Logical Ideas
• Math Origins: The Logical Symbols

Teaching and Learning the Trigonometric Functions through Their Origins

A series of curricular units by Daniel E. Otero based on primary source texts for use in teaching and learning trigonometry.

• Series Introduction
• Episode 1 - Babylonian Astronomy and Sexagesimal Numeration
• Episode 2 - Hipparchus’ Table of Chords
• Episode 3 - Ptolemy Finds High Noon in Chords of Circles
• Episode 4 – Varāhamihira and the Poetry of Sines

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 π: 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
• 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

HOM SIGMAA Student Contest Winning Papers

• 2020: Jeffrey Powers (Grand Rapids Community College), “Did Archimedes Do Calculus?”
• 2019: Amanda Nethington (University of Missouri – Kansas City), "Achieving Philosophical Perfection: Omar Khayyam's Successful Replacement of Euclid's Parallel Postulate."
• 2018: First place – Callie Lane (University of Missouri – Kansas City), "Race to Refraction: The Repeated Discovery of Snell's Law"; Second place – Christen Peters (Lee University), "The Reality of the Complex: The Discovery and Development of Imaginary Numbers," and Rachel Talmadge (University of Missouri – Kansas City), "François Viète Uses Geometry to Solve Three Problems."
• 2017: Co-winners – Amanda Akin (Lee University), “To Infinity and Beyond: A Historical Journey on Contemplating the Infinite,” Johann Gaebler (Harvard University), “Traditionalism: 1894 to 1925,” and Nathan Otten (University of Missouri – Kansas City), “Huygens and The Value of all Chances in Games of Fortune.”
• 2016: Co-winners – Brittany Anne Carlson (Salt Lake Community College), “A Latent Element of Alice’s Agency in Wonderland: Conservative Victorian Mathematics,” and William Cole (Lee University), “The Evolution of the Circle Method in Additive Prime Number Theory.”
• 2015: Co-winners – Samuel Patterson (University of Missouri – Kansas City), “Bernard Bolzano, a Genius Unnoticed in His Time,” and Briana Yankie (Lee University), “Examining Disproved Mathematical Ideas through the Lens of Philosophy.”
• 2014: First place – Jenna Miller (University of Missouri – Kansas City), "Casting Light on the Statistical Life of Florence Nightingale," and Anna Riffe (University of Missouri – Kansas City), "The Impossible Proof: An Analysis of Adrien-Marie Legendre's Attempts to Prove Euclid's Fifth Postulate"; Second place – Paul Ayers (University of Missouri – Kansas City), “Gabriel Cramer: Over 260 Years of Crushing the Unknowns," and Mary Ruff (Colorado State University – Pueblo), "Probability to 1750."
• 2013: Matthew Shives (Hood College), "Paradigms and Mathematics: A Creative Perspective."
• 2012: First place – Jesse Hamer (University of Missouri – Kansas City), “Indivisibles and the Cycloid in the Early 17th Century”; Second place – Kevin L. Wininger (Otterbein University), “On the Foundations of X-Ray Computed Tomography in Medicine: A Fundamental Review of the 'Radon transform' and a Tribute to Johann Radon.”
• 2011: First place – Paul Stahl (University of Missouri – Kansas City), “Kepler's Development of Mathematical Astronomy”; Second place – Sarah Costrell (Brandeis University), “Mathematics and Mathematical Thought in the Quadrivium of Isidore of Seville,” and Rick Hill (University of Missouri – Kansas City), “Thomas Harriot's Artis Analyticae Praxis and the Roots of Modern Algebra.”
• 2010: Co-winners – Jennifer Nielsen (University of Missouri – Kansas City), “The Heart is a Dust Board:  Abu’l Wafa Al-Buzjani, Dissection, Construction, and the Dialog Between Art and Mathematics in Medieval Islamic Culture,” Palmer Rampell (Phillips Academy and Harvard University), “The Use of Similarity in Old Babylonian Mathematics,” and Stefanie Streck (Pacific Lutheran University), “The Fermat Problem.”
• 2009: First place – Nathan McLaughlin (University of Montana), “The Mathematical Optics of Sir William Hamilton: Conical Refraction and Quaternions”; Second place – Tim Chalberg (Pacific Lutheran University), “Regression Analysis: A Powerful Tool and Riveting Drama”; Honorable Mention – Amy Buchmann (Chapman University), “A Brief History of Quaternions and the Theory of Holomorphic Functions of Quaternionic Variables.”
• 2008: First place – Mame Maloney (University of Chicago), “Constructivism: A Realistic Approach to Math?”; Second place – Woody Burchett (Georgetown College), “Thinking Inside the Box: Geometric Interpretation of Quadratic Problems in BM 13901,” and Cole McGee (Colorado State University – Pueblo), “Jean Le Rond D'Alembert: Biography of a Mathematician, Philosophe, and a Man of Letters”; Honorable mention – Mame Maloney (University of Chicago), “Pathological Functions in the 18th and 19th Centuries.”
• 2007: Co-winners – Rory Plante, “The Libra Astronomica and its Mathematics,” and Douglas Smith (Miami University, Ohio), “Lucas’s theorem: A Great Theorem.”
• 2006: Co-winners – Jennifer Wiegert, “The Sagacity of Circles: A History of the Isoperimetric Problem,” and Samantha Reynolds (University of Missouri – Kansas City), “Maria Gaetana Agnesi: Female Mathematician and Brilliant Expositor of the 18^th Century.”
• 2005: First place – Newlyn Walkup (University of Missouri – Kansas City), “Eratosthenes and the Mystery of the Stades”; Second place – James Collingwood (Drake University), “Rigor in Analysis: From Newton to Cauchy.”
• 2004: Co-winners – Mark Walters, “It Appears That Four Colors Suffice: A Historical Overview of the Four-Color Theorem,” and Heath Yates (University of Missouri – Kansas City), “An Emanji Temple Tablet.”