What's in Convergence? - Contents of Volume 3 - 2006

Editors: Victor J. Katz, Frank J. Swetz

Articles

The Rule of False Position and Geometric Problems, by Vicente Meavilla Segui and Alfinio Flores

This article contains examples of the use of the rule of false position in the solution of geometric problems as found in the work of Simon Stevin. We discuss the benefits for future teachers and their students.

Approximate Construction of Regular Polygons: Two Renaissance Artists, by Raul A. Simon

Leonardo da Vinci and Albrecht Durer both offered approximate constructions of regular pentagons for the use of artists. This article explains these constructions.

John Napier: His Life, His Logs, and His Bones, by Michael J. Caulfield

A brief introduction to the life of John Napier, along with an animation of calculations using Napier's bones.

The Sagacity of Circles: A History of the Isoperimetric Problem, by Jennifer Wiegert

A summary of the history of the problem of finding the region of greatest area bounded by a given perimeter. This essay was a winner of the HOM SIGMAA Student Paper Contest in 2006.

Gerbert d'Aurillac and the March of Spain: A Convergence of Cultures, by Betty Mayfield

The story of Gerbert, who became Pope Sylvester II in 999, and his mathematics.

Dear Professor Greitzer, by Joe Richards and Don Crossfield

A letter to Sam Greitzer, late editor of Arbelos, discussing the derivation of two formulas for calculating pi.

The Quadrature of the Circle and Hippocrates’ Lunes, by Daniel E. Otero

A study of some elements of Greek geometry, as part of a course for liberal arts undergraduates dealing with basic concepts of the calculus.

An Investigation of Historical Geometric Constructions, by Suzanne Harper and Shannon Driskell

Dynamic geometry software is used to demonstrate early Greek attempts at the trisection of an angle and the squaring of a circle.

The Great Calculation According to the Indians of Maximus Planudes, by Peter G. Brown

A translation of part of a thirteenth century work by the Byzantine monk Maximus Planudes on the Hindu-Arabic numerals and the algorithms for calculation.

Fibonacci and Square Numbers, by Patrick Headley

A discussion of aspects of Leonardo of Pisa's Book of Squares.

Leonard Euler’s Solution to the Konigsberg Bridge Problem, by Teo Paoletti

A survey of the famous Konigsberg Bridge Problem and its connection to graph theory by an undergraduate student.

A Plague of Ratios, by Benjamin Wardhaugh

The story of Nicolaus Mercator, music, and logarithms.

Student Reports: A Rewarding Undertaking, by Frank J. Swetz

Some ideas on using student reports when you teach a course in the history of mathematics

How Tartaglia Solved the Cubic Equation, by Friedrich Katscher

The method of Tartaglia for solving cubics, that he eventually explained to Cardano.

Who Was Tartaglia Really?, by Friedrich Katscher

In many sources, we see that Tartaglia has the surname Fontana. According to the author of this article, the co-discoverer of the cubic formula did not ever use that name.

Announcements

Karen Dee Michalowicz, by Victor J. Katz

We sadly announce the untimely death of one of Convergence's editorial board members.

From the Editors, by Victor J. Katz and Frank Swetz

The editors invite contributions, participation, and feedback from Convergence readers.

Reviews

From Calculus to Computers: Using the Last 200 Years of Mathematics History in the Classroom, edited by Amy Shell-Gellasch and Dick Jardine. Reviewed by Jim Kiernan.

A collection of articles on using the history of mathematics of the past 200 years in the undergraduate classroom.

The Joy of Pi, by David Blatner. Reviewed by Frank J. Swetz.

A highly recommended new book on the history and applications of pi.

Joy of Pi Website. Reviewed by Jon Choate.

This website is connected to the book, The Joy of Pi. It has numerous interesting facts about pi, with links to additional sites.

Negative Math: How Mathematical Rules Can Be Positively Bent, by Alberto A. Martinez. Reviewed by Karen Michalowicz.

The story of the negative numbers.

The Archimedes Website. Reviewed by Marcus Barnes.

This website devoted to miscellanea about Archimedes contains much interesting material about his life and times.

The Equation that Couldn't Be Solved, by Mario Livio. Reviewed by Doris Schattschneider.

A history of attempts to solve cubic and higher degree polynomial equations, including the notions of group theory and their relationship to the idea of symmetry.

The Square Root of 2: A Dialogue Concerning a Number and a Sequence, by David Flannery. Reviewed by Barnabas Hughes.

A wonderful book about the square root of 2, beginning with the search for the side of a square double a given square.

A Contextual History of Mathematics, by Ronald Calinger. Reviewed by Frank J. Swetz.

An overly ambitious textbook on the history of mathematics.

The Prince of Mathematics: Carl Friedrich Gauss, by M. B. W. Tent. Reviewed by Linda Y. Shuey.

A biography of Gauss designed for high school students.

The History of Mathematics: A Brief Course, by Roger Cooke. Reviewed by Gary Stoudt.

A new edition of a brief history text, arranged topically rather than chronologically.

Awakening of Geometrical Thought in Early Culture, by Paulus Gerdes. Reviewed by Lawrence Shirley.

How does geometry begin? This work explores the origins of geometry in the work of artisans.

The Honors Class: Hilbert’s Problems and Their Solvers, by Ben H. Yandell. Reviewed by Frank J. Swetz.

This work discusses the people who solved some of Hilbert's problems from 1900, as well as the mathematics involved in the solutions.

Math Forum Website. Reviewed by Gail Kaplan.

A description of this well-regarded website.

Math Pages Website. Reviewed by Laura Smith.

A general mathematics website with much information on the history of mathematics.

Ancient Mathematics, by Serafina Cuomo. Reviewed by Barnabas Hughes.

A new history of Greek mathematics, taking into account the latest research.

History of Mathematics Archive Website. Reviewed by Don Crossfield.

A wide-ranging site with links to many sources in the history of mathematics.

ABOUT Website on History of Mathematics. Reviewed by Lawrence Shirley.

A section of a much larger website, dealing with some random topics in the history of mathematics.

Mathematics and The Historian’s Craft: The Kenneth O. May Lectures, edited by G. Van Brummelen and M. Kinyon. Reviewed by Jon Choate.

A collection of the Kenneth May lectures in the history of mathematics given at meetings of the Canadian Society for the History and Philosophy of Mathematics.

Thinking about Mathematics: The Philosophy of Mathematics, by Stewart Shapiro. Reviewed by Frank J. Swetz.

An excellent book surveying the history of the philosophy of mathematics from the time of Plato to the nineteenth and early twentieth centuries.