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

Need the Area of a Triangle? The Pope Can Help! by Betty Mayfield
Gerbert d’Aurillac on finding the area of an equilateral triangle, with exploration activities for students. (posted 11/28/2022)

Ongoing Series

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
• James Joseph Sylvester
• Nicolaus Copernicus
• 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 Second-Semester 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 2023:

• Christiaan Huygens’s Horologium Oscillatorium (1673)
• James Clerk Maxwell’s Treatise on Electricity and Magnetism (1873)
• 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)