*Editors:* Victor J. Katz, Frank J. Swetz, Janet Beery, Kathleen Clark

### Articles

James Gregory and the Pappus-Guldin Theorem, by Andrew Leahy

An analysis of James Gregory's proof of the Pappus-Guldin Theorem, along with the original documents in both Latin and English.

A Locally Compact REU in the History of Mathematics: Involving Undergraduates in Research, by Betty Mayfield and Kimberly Tysdal

A description of a Research Experience for Undergraduates conducted in 2007 at Hood College.

Sums of Powers of Positive Integers, by Janet Beery

A history of attempts to develop formulas expressing the sums of powers of the first *n* positive integers from the Pythagoreans to Jakob Bernoulli.

Investigating Euler's Polyhedral Formula Using Original Sources, by Lee Stemkoski

The works of Leonhard Euler are particularly accessible to readers as his papers usually contain many examples as well as a gradual progression of ideas. The author shows how teachers can use Euler's original works in the classroom to explore the polyhedral formula and related results.

HOM SIGMAA 2009 Award Winners, by Amy Shell-Gellasch

These are the winning papers from the annual History of Mathematics Special Interest Group of the MAA (HOM SIGMAA) 2009 Student Paper Contest.

A Modern Vision of the Work of Cardano and Ferrari on Quartics, by Harald Helfgott and Michel Helfgott

A study of the solution of quartic equations in Cardano's *Ars Magna* and in the work of Euler and Descartes.

The Classic Greek Ladder and Newton’s Method, by Robert J. Wisner

Greek ladders for approximating square roots may be more ancient than the ancient Greeks. Students at any level can appreciate their beauty and simplicity. Those who have studied calculus can compare them with Newton’s Method for approximating roots.

“In these numbers we use no fractions”: A Classroom Module on Stevin’s Decimal Numbers, by Kathleen Clark

After completing this assignment on Simon Stevin's treatment of decimal numbers in his 1585 *De Thiende,* the author's preservice mathematics teachers understood why our usual procedure for multiplying such numbers works.

### Reviews

*The Mayan and Other Ancient Calendars,* by Geoff Stray. Reviewed by Lawrence Shirley.

A detailed study of the cycles of the Mayan calendar, along with some other ancient calendars.

*Euler's Gem: The Polyhedron Formula and the Birth of Topology,* by David S. Richeson. Reviewed by Clifford Wagner.

A sketch of the history of topology, beginning with the polyhedron formula and continuing up to the present.

*Mathematics in India,* by Kim Plofker. Reviewed by Frank J. Swetz.

A survey of over two thousand years of the history of mathematics on the Indian subcontinent.

*The Mathematics of the Heavens and the Earth: the Early History of Trigonometry,* by Glen Van Brummelen. Reviewed by Frank J. Swetz.

A comprehensive history of trigonometry from ancient times to the Renaissance.

*Mathematical Works Printed in the Americas, 1554-1700,* by Bruce Stanley Burdick. Reviewed by Frank J. Swetz.

A bibliographical reference to mathematics books printed in the New World before 1700.

*Mathematicians: An Outer View of the Inner World,* by Mariana Cook. Reviewed by Frank J. Swetz.

Portraits of 92 living mathematicians, with autobiographical comments.

*Pythagoras' Revenge: A Mathematical Mystery,* by Arturo Sangalli. Reviewed by James F. Kiernan.

A fictionalized account of Pythagoras and Pythagorean beliefs.

*Euclidean and Non-Euclidean Geometries: Development and History,* by Marvin Jay Greenberg. Reviewed by Eugene Boman.

This textbook seamlessly combines the history of non-Euclidean geometry with the mathematical ideas.