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What's in Convergence? - Contents of Volume 11 - 2014

Editor:  Janet Beery

Associate Editors: Amy Ackerberg-Hastings, Janet Barnett, Kathleen Clark, Lawrence D'Antonio, Douglas Ensley, Victor Katz, Daniel Otero, Randy Schwartz, Lee Stemkoski, Frank Swetz

Founding Editors: Victor Katz, Frank Swetz

Articles

An Investigation of Subtraction Algorithms from the 18th and 19th Centuries, by Nicole M. Wessman-Enzinger

This survey of four subtraction algorithms used in North America includes as sources both handwritten "cyphering books" and printed arithmetic texts.


Connecting Greek Ladders and Continued Fractions, by Kurt Herzinger and Robert Wisner

An exploration of two historical techniques for estimating irrational numbers and a link between them


Did Euler Know Quadratic Reciprocity?: New Insights from a Forgotten Work, by Paul Bialek and Dominic W. Klyve

The authors use their newly translated paper of Leonhard Euler to answer their title question.


Cubes, Conic Sections, and Crockett Johnson, by Stephanie Cawthorne and Judy Green

Author and illustrator Johnson, author of Harold and the Purple Crayon, posed a question about Euclid, cubes, and conic sections, and painted an answer!


When Nine Points Are Worth But Eight: Euler's Resolution of Cramer's Paradox, by Robert Bradley and Lee Stemkoski

Interactive graphics illustrate the seeming paradox that 9 points should determine a curve of order 3, yet two curves of order 3 can intersect in up to 9 distinct points.


David Hilbert's Radio Address, by James T. Smith

Read and listen to this famous 1930 address, with its dramatic conclusion: "Wir müssen wissen; wir werden wissen." ("We must know; we will know.")


HOM SIGMAA 2014 Student Paper Contest Winners

Read winning student papers on the statistics of Florence Nightingale and on Legendre's attempts to prove Euclid's Fifth Postulate.


Celebrating a Mathematical Miracle: Logarithms Turn 400, by Glen Van Brummelen

Why John Napier's invention of logarithms in 1614 was hailed as a miracle by astronomers and mathematicians


Wibold's Ludus Regularis, a 10th Century Board Game, by Richard Pulskamp and Daniel Otero

Players competed for virtues in this dice game for clerics.


How to Improve a Math History Assignment, by Christopher Goff

Moving college students' original source mathematics history projects beyond "reporting" to "engagement"


Historical Activities for the Calculus Classroom, by Gabriela R. Sanchis

History and mathematics of curve sketching, tangent lines, and optimization, explored using interactive applets


A Pair of Articles on the Parallelogram Theorem of Pierre Varignon, by Peter N. Oliver

Mathematical life of Varignon, plus ideas for classroom activities and extensions of his famous theorem


Mathematical Treasures from the National Museum of American History, Smithsonian Institution


Mathematical Treasures III, by Frank J. Swetz

Review

Review of Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World, by Amir Alexander. Reviewed by Frank J. Swetz.

How 17th century European proponents of indivisibles and infinitesimals clashed with Thomas Hobbes, Christopher Clavius, and the Catholic Church

 

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