What's in Convergence? - Contents of Volume 20 - 2023

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.

• Series Introduction
• Fermat’s Integration of Powers

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.

• Series Introduction
• The Quadrature of the Parabola: An Ancient Theorem in Modern Form, by Carl Boyer with commentary by William Dunham

Quotations in Context, by Michael Molinsky
A series of columns that explores the origins and meanings of various quotations about mathematics and mathematicians.

• Series Introduction
• Albert Einstein
• Alfred North Whitehead
• Bertrand Russell
• Charles Darwin
• James Joseph Sylvester
• John Adams
• Nicolaus Copernicus
• Oliver Wendell Holmes, Jr.
• Plato

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.

• Series Purpose and Structure, by Amy Ackerberg-Hastings
• Introduction to Historiography and Methodology, by Amy Ackerberg-Hastings

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.

• Series Introduction, by Peggy Aldrich Kidwell
• 19th-century String Models, by Peggy Aldrich Kidwell
• Andean Khipus, by Manuel Medrano

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)