*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

Unreasonable Effectiveness of Knot Theory, by Mario Livio

Knot theory has become surprisingly useful in explaining string theory.

Proofs Without Words and Beyond, by Tim Doyle, Lauren Kutler, Robin Miller, and Albert Schueller

History and philosophy of visual proofs, together with dynamic, interactive "proofs without words 2.0"

Van Schooten's Ruler Constructions, by C. Edward Sandifer

Translation of and commentary on Frans van Schooten's work on constructions using only a straightedge -- and a postulate that allows the copying of one line segment onto another.

Led Astray by a Right Triangle: Misconception, Epiphany, and Redemption, by Frank J. Swetz

A well-known historian initially erred in his study of ancient Chinese mathematics.

Euclid21: Euclid's *Elements* for the 21st Century, by Eugene Boman, Alexandra Milbrand, Tyler Brown, Siddharth Dahiya, Joseph Roberge, and Mary Boman

A dynamic, interactive Euclid's *Elements* organized as a directed graph via its logical structure

Online Museum Collections in the Mathematics Classroom, by Amy Ackerberg-Hastings and Amy Shell-Gellasch

The Smithsonian Institution's National Museum of American History website features dozens of object groups, collections of digitized object images and detailed catalog records, related to mathematics. View sample objects and read suggestions for using these resources in your teaching.

Mathematical Treasures from the National Museum of American History, Smithsonian Institution, by Amy Ackerberg-Hastings, Judy Green, Peggy Kidwell, and Amy Shell-Gellasch

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