*Editors:* Victor J. Katz, Frank J. Swetz

### Articles

Euler Squares, by Elaine Young

An elementary introduction to Euler squares

Maya Cycles of Time, by Sandra Monteferrante

Explorations of the Mayan calendar

Abel on Elliptic Integrals: A Translation, by Marcus Emmanuel Barnes

A translation of one of the seminal papers in the field of elliptic integrals, but one that can be read by an undergraduate.

Limit Points and Connected Sets in the Plane, by David R. Hill and David E. Zitarelli

A study of Mullikan's Nautilus, using movies to illustrate the important ideas

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

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

Proportionality in Similar Triangles: A Cross-Cultural Comparison, by Jerry Lodder

A comparison of the Greek and Chinese approach to the idea of similarity.

The Unique Effects of Including History in College Algebra, by G. W. Hagerty, S. Smith, D. Goodwin

Using the history of mathematics in a college algebra class has had significant positive effects on student learning.

Episodes in the History of Geometry through Models in Dynamic Geometry, by Eduardo Veloso and Rita Bastos

Four episodes in the history of geometry are discussed, where dynamic geometry helps in understanding the ideas.

HOM SIGMAA 2007 Student Paper Contest Winners

Research earning awards in HOM SIGMAA's annual competition.

### Announcements

Euler Tercentenary Year, by Victor J. Katz

2007 marks the three hundredth anniversary of the birth of Leonhard Euler, the most prolific mathematician of all time. There are numerous events throughout the world celebrating this anniversary, many of which are listed here.

2008 Joint Mathematics Meetings, by Victor J. Katz

There are numerous mathematics history events at the upcoming AMS-MAA Joint Mathematics Meetings in San Diego, CA.

### Reviews

*Great Feuds in Mathematics,* by Hal Hellman. Reviewed by Jim Kiernan.

A lively description of ten of the greatest feuds in mathematics.

*History of Mathematics,* by Charles Boyer and Uta Merzbach. Reviewed by Kathleen Acker.

Boyer's classic text, as revised by Uta Merzbach, is still worth having.

*A Concise History of Mathematics,* by Dirk J. Struik. Reviewed by Barnabas Hughes.

The classic work by Dirk Struik is still worth reading, especially for its attention to the social context of the development of mathematical ideas

*God Created the Integers: Mathematical Breakthroughs that Changed History,* edited by Stephen Hawking. Reviewed by Eugene Boman.

Original source material from seventeen mathematicians, with commentary by Stephen Hawking

*Pioneers in Mathematics,* by Michael J. Bradley. Reviewed by Linda Y. Shuey.

A five volume set of biographies of mathematicians from ancient times to the twentieth century, aimed at secondary students.

*Arthur Cayley: Mathematician Laureate of the Victorian Age,* by Tony Crilly. Reviewed by Kathleen M. Clark.

A biography of Arthur Cayley, the outstanding mathematician of Victorian Britain

*King of Infinite Space: Donald Coxeter, the Man Who Saved Geometry,* by Siobhan Roberts. Reviewed by Jonathan Choate.

A biography of the geometer Donald Coxeter.

*A Radical Approach to Real Analysis,* by David Bressoud. Reviewed by James Callahan.

A historically minded textbook designed to teach real analysis by considering some of the problems faced by 19th century mathematicians.

*Unknown Quantity; A Real and Imaginary History of Algebra,* by John Derbyshire. Reviewed by Don Crossfield.

A history of algebra from its early beginnings to the twentieth century.

*Equations from God: Pure Mathematics and Victorian Faith,* by Daniel J. Cohen. Reviewed by Barnabas Hughes.

A study of Victorian idealism and its relation to religion, as exemplified in the work of three 19th century British mathematicians.

*An Introduction to the History of Mathematics,* by Howard Eves. Reviewed by Gary Stoudt.

Howard Eves' sixth edition is still worth considering for a textbook.

*The Secret Life of Numbers,* by George G. Szpiro. Reviewed by Edith Prentice Mendez.

Short sketches on how mathematicians work and think.

*Prime Numbers: The Most Mysterious Figures in Math,* by David Wells. Reviewed by Gabriela R. Sanchis.

An introduction to the prime numbers in many of their aspects.

*James Joseph Sylvester: **Jewish Mathematician in a Victorian World,* by Karen Hunger Parshall. Reviewed by Gail Kaplan.

The first detailed biography of James Joseph Sylvester.

*Yearning for the Impossible: The Surprising Truths of Mathematics,* by John Stillwell. Reviewed by Lynn Godshall.

This book explores the history of mathematics from the perspective of the creative tension between common sense and the "impossible" as the author follows the discovery or invention of new concepts that have marked mathematical progress.

Euler Tercentenary Volumes 1 and 2:

*The Early Mathematics of Leonhard Euler,* by C. Edward Sandifer.

*The Genius of Euler: Reflections on his Life and Work,* edited by William Dunham.

Reviewed by Frank J. Swetz.

Two excellent volumes on Euler in honor of his three hundredth birthday.

*Unexpected Links between Egyptian and Babylonian Mathematics,* by Jöran Friberg. Reviewed by Lawrence Shirley.

This book demonstrates the relationship between the mathematics in some recently discovered Babylonian tablets and some standard problems from Egyptian mathematics.

*Measuring America,* by Andro Linklater. Reviewed by Frank J. Swetz.

The beginnings of land measurement in the early United States and how this affected American democracy.

*The Life of Numbers,* written by Alberto Manguel, Antonio Duran and George Ifrah; illustrated by Sean Macksouli, Natalia Pintado, and Javier Pagola. Reviewed by Frank J. Swetz.

A creative expression combining text, design and illustrations, originally designed for the International Congress of Mathematicians in Madrid.

*Amazing Traces of a Babylonian Origin in Greek Mathematics,* by Jöran Friberg. Reviewed by Barnabas Hughes.

Aspects of classical Greek mathematics are compared with areas of Babylonian mathematics.

*The Poincare Conjecture: In Search of the Shape of the Universe,* by Donal O’Shea. Reviewed by Eugene Boman.

The history of the Poincare conjecture up to its recent proof by Grigori Perelman.

Euler Tercentenary Volume 3:

*How Euler Did It,* by C. Edward Sandifer. Reviewed by Frank J. Swetz.

A collection of short pieces each detailing how Euler solved a particular mathematics problem.

*A History of Mathematics,* by Jeff Suzuki. Reviewed by Gary Stoudt.

A solid history of mathematics text that any instructor of a history course should consider.

*The Development of Mathematics in Medieval Europe,* by Menso Folkerts. Reviewed by Frank J. Swetz.

A collection of articles on mathematics in Europe from the twelfth to the fifteenth century.

*The Pythagorean Theorem: A 4,000 Year History,* by Eli Maor. Reviewed by Jim Kiernan.

A survey of this theorem's 4000 year history, with applications to many fields.

*Mathematics: Powerful Patterns in Nature and Society,* by Harry Henderson. Reviewed by Linda Y. Shuey.

The work of ten scientists who thought deeply about patterns.

*The Mathematics of Egypt, Mesopotamia, China, India and Islam,* edited by Victor J. Katz. Reviewed by Barnabas Hughes.

A new collection of original source materials in the mathematics of five civilizations.

*Calculus Gems: Brief Lives and Memorable Moments,* by George F. Simmons. Reviewed by Kathleen M. Clark.

A collection of short biographical sketches of people involved in the development of calculus, as well as brief descriptions of important events in that development.

Euler Tercentenary Volumes 4 and 5:

*Euler and Modern Science,* edited by N.N. Bogolyubov, G.K. Mikhailov, and A.P. Yushkevich.

*Euler at 300: An Appreciation,* edited by Robert Bradley, Lawrence D’Antonio, and C. Edward Sandifer.

Reviewed by Frank J. Swetz.

The two final volumes of the MAA tercentenary series on Euler present numerous papers on various aspects of Euler's life and work.

*The Mathematician's Brain,* by David Ruelle. Reviewed by Kathleen Acker.

A book delving into the working of the mathematical mind.

*How Mathematics Happened: The First 50,000 Years,* by Peter S. Rudman. Reviewed by Gail Kaplan.

A popular history of ancient mathematics, dealing with the mathematics of ancient Egypt and Babylonia.

*Math for Mystics: From the Fibonacci Sequence to Luna's Labyrinth to the Golden Section and Other Secrets of Sacred Geometry,* by Renna Shesso. Reviewed by Edith Prentice Mendez.

A book connecting mathematics to mysticism, but not recommended.

*Numbers at Work: A Cultural Perspective,* by Rudolf Taschner. Reviewed by Jonathan Choate.

Essays on how number has been critical to the work of scientists through the ages.

*Hypatia of Alexandria: Mathematician and Martyr,* by Michael A. B. Deakin. Reviewed by Eugene Boman.

A biography of Hypatia in her times that carefully distinguishes between the known facts of her life and the many speculations about her.