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There are in this world optimists who feel that any symbol that starts off with an integral sign must necessarily denote something that will have every property that they should like an integral to possess. This of course is quite annoying to us rigorous mathematicians; what is even more annoying is that by doing so they often come up with the right answer.

Bulletin of the American Mathematical Society, v. 69, p. 611, 1963.

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# What's in Convergence?

## Contents of Volume 1 - 2004

Editors: Victor J. Katz, Frank J. Swetz

Articles

Using Problems from the History of Mathematics, by Frank Swetz

Why should we use historical problems in today's classroom? This article answers that question and serves as an introduction to the problems on this website.

Can You Really Derive Conic Formulae from a Cone?, by Gary S. Stoudt

As is the case with a great deal of interesting mathematics, the conic sections are believed to have been discovered in an attempt to solve a problem, a problem that on the surface seems to have nothing to do with conic sections.

Benjamin Banneker's Trigonometry Puzzle, by Florence Fasanelli, Graham Jagger, and Bea Lumpkin

Benjamin Banneker solved some trigonometry problems in his extant notebooks. One of them is discussed here. The authors have also discovered the probable source of Banneker's trigonometry table.

Euler's Analysis of the Genoese Lottery, by Robert E. Bradley

In the middle of the 18th century, King Frederick the Great of Prussia became interested in creating a lottery to raise money. As was his custom when mathematical matters were involved, he called upon Leonhard Euler for counsel.

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

A translation of and commentary on Frans van Schooten's work on constructions using only a straightedge. Van Schooten's postulates for use of the straightedge, however, allow the copying of one line segment onto another.

Measuring the Globe: An Historical Activity, by Barnabas Hughes

Eratosthenes' measurement of the earth, in a form that's easy for teachers to use.

A Euclidean Approach to the FTC, by Andrew Leahy

The Fundamental Theorem of Calculus is presented in the version of Scottish mathematician James Gregory -- without the use of limits.

The Right and Lawful Rood, by Peter Ransom

The "rood", a linear measure dating from many centuries ago, is calculated anew in today's classrooms.

Using Historical Problems in the Middle School, by Karen Michalowicz and Robert McGee

Historical problems can be used to enliven any mathematics class. Here are some examples from medieval times, from a 19th century American textbook, and from a 19th century Armenian textbook, among other sources.

Alien Encounters, by Gavin Hitchcock

A dramatization, in two Acts, of the struggles of European mathematicians of the seventeenth and eighteenth centuries to come to terms with the newly admitted negative numbers.

Mathematics as the Science of Patterns, by Michael N. Fried

Mathematics is often referred to today as the "science of patterns." But has this always been true historically, or is this something that happened in recent times? The question is discussed here with reference to the work of Euclid and Jacob Steiner.

Counting Boards, by Chris Weeks

The author finds a rare and fine example of a counting table in Strasbourg. Article contains two photos of this table.

Teaching Leonardo: An Integrated Approach, by Rick Faloon

The work of the great Renaissance artist/scientist Leonardo da Vinci can be taught in secondary schools through an integrated approach of several disciplines. This article explores the approach of the Ross School.

Reviews

Sherlock Holmes in Babylon, edited by Marlow Anderson, Victor Katz and Robin Wilson. Reviewed by Frank J. Swetz

A collection of articles in the history of mathematics that appeared in journals of the Mathematical Association of America over the past 90 years.

Famous Problems and Their Mathematicians, by Art Johnson. Reviewed by Frank J. Swetz

This resource consists of a series of 61 worksheets, each focused on a particular problem and related to a particular historical mathematical personality.

Stamping Through Mathematics, by Robin Wilson. Reviewed by Tim Keenan

The author takes us on a historical tour of mathematics through postage stamps of the world that display mathematicians and mathematics.

St. Andrews History of Mathematics Archive Website  Reviewed by Barnabas Hughes

This website offers a collection of biographies of mathematicians and a variety of resources on the development of various branches of mathematics. It is an extremely rich and extensive site.

Statisticians of the Centuries, edited by C. C. Heyde and E. Seneta. Reviewed by Winston Richards

Thumbnail sketches of statisticians throughout history.

Historical Connections in Mathematics, by Wilbert Reimer and Luetta Reimer. Reviewed by Frank J. Swetz

Brief biographies of mathematicians with mathematical activities based on their work.

Multicultural Classroom Posters Sets 3 & 4  Reviewed by by Vincent Corrado

These posters illustrate aspects of the history of mathematics in countries from Babylonia to Ireland.

Celebrating Women in Mathematics and Science, by Miriam P. Cooney. Reviewed by Erica Voolich

This unique and beautiful book features the biographies of twenty-two notable female mathematicians and scientists, showing how their determination, creativity, and intellectual passion helped them excel in their fields.

Agnesi to Zeno, by Sanderson Smith. Reviewed by Linda Shuey

Short biographies of mathematicians with mathematical activities.

Euler: The Master of Us All, by William Dunham. Reviewed by Clifford Wagner

A small selection of Euler's works, explained by a master expositor.

Mathematics Elsewhere, by Marcia Ascher. Reviewed by Lawrence Shirley

A compilation of ethnomathematical ideas from around the world.

Four Colors Suffice, by Robin Wilson. Reviewed by Frank J. Swetz

The history of the four color problem with sketches of the attempted proofs in the nineteenth century and an outline of the computer proof of the twentieth century.

Historical Topics for the Mathematics Classroom, edited by J.K. Baumgart, D.E. Deal, B.R. Vogeli, and A.E. Hallerberg. Reviewed by Tim Keenan

This 1989 revision of the 1969 NCTM yearbook still provides wonderful suggestions for using the history of mathematics in the classroom.

The Art of the Infinite, by Robert Kaplan and Ellen Kaplan. Reviewed by Albert Briggs

This book is a collection of mathematical ideas organized around the themes of infinity and the illumination of the nature of mathematical thought.

Number from Ahmes to Cantor, by Midhat Gazalé. Reviewed by Frank J. Swetz

A lively history of number systems and number theory from earliest times up to the notion of "infinity".

Milestones of Mathematics Posters  Reviewed by Lynn Godshall

Two posters illustrating the major milestones in the history of mathematics, from the first ideas of "number" to the proof of Fermat's Last Theorem.

The Nothing That Is, by Robert Kaplan. Reviewed by Austin Lobo

A history of the concept of zero from as far back as the Babylonian period, with philosophical excursions into the meaning of "nothing".

The Saga of Mathematics, by Marty Lewinter and William Widulski. Reviewed by Jim Kiernan

A brief history of mathematics aimed at college students with little technical knowledge of mathematics.

Multicultural Classroom Posters Sets 1 & 2  Reviewed by Lynn Godshall

Posters illustrating mathematics concepts in such places as China, Japan, India, and the Americas.

Historic Women of Mathematics Poster  Reviewed by Karen Michalowicz

Poster picturing five famous women, from Hypatia to Grace Hopper.

Benjamin Banneker Poster  Reviewed by Karen Michalowicz

Poster of Banneker, with a brief description of his life and work.

Consortium's Historical Notes  Reviewed by Jim Kiernan

Collection of historical articles that appeared in Consortium, the newsletter of COMAP.

Remarkable Mathematicians, by Ioan James. Reviewed by Jim Kiernan

A collection of biographies of sixty mathematicians from the eighteenth century to the twentieth.

Colorful Characters of Mathematics Posters, by Isaac Asimov. Reviewed by Art Johnson

Whimsical posters of fifteen mathematicians with brief biographies.

The Pioneers of Calculus Posters, by Bruce White. Reviewed by Art Johnson

A collection of sixteen posters of contributors to calculus, with brief biographical sketches.

Great Ideas of Mathematics Posters  Reviewed by Sylvia Lazarnick

A set of four posters dealing with the Pythagorean Theorem, infinity, prime numbers, and the history of pi.

Speaking of Mathematics Posters  Reviewed by Lynn Godshall

A collection of 24 mini-posters, each containing a quotation about mathematics.

Archimedes: What Did He Do Besides Cry Eureka?, by Sherman Stein. Reviewed by Tim Keenan

Archimedes' work, The Method, explained, along with many other important ideas of the great Greek geometer.

A History of Analysis, edited by Hans Niels Jahnke. Reviewed by Jeff Suzuki

A superb collection of articles by experts on various areas of the history of analysis, from the Greeks to modern times.

Readings in the History of Mathematics Education, by James K. Bidwell and Robert G. Clason. Reviewed by Lynn Godshall

This collection of readings gives details on the history of mathematics education in the U.S. from 1828 to 1959.

Mathematical Evolutions, edited by Abe Shenitzer and John Stillwell. Reviewed by Lang Moore

A collection of articles from the American Mathematical Monthly by experts on the evolution of various fields of mathematics.

The Mathematical Century, by Piergiorgio Odifreddi. Reviewed by Gary Stoudt

The development of 30 important mathematics subjects during the twentieth century made understandable to undergraduate mathematics majors.

The Story of Mathematics, by Richard Mankiewicz. Reviewed by Anne Loesch

A wonderful survey of the history of mathematics, emphasizing its relationship with the ambient culture.

Great Moments in Mathematics Before 1650, by Howard Eves. Reviewed by Jon Choate

A collection of short lectures by Howard Eves giving details on 20 important happenings in the history of mathematics before 1650.

Cogwheels of the Mind: The Story of Venn Diagrams, by A. W. F. Edwards. Reviewed by Jim Kiernan

An introduction to the work of Venn as well as the work of the author in extending some of Venn's results.

Abel's Proof, by Peter Pesic. Reviewed by by Lynn Godshall

A discussion of the meaning of mathematical unsolvability in the context of the history of Abel's proof of the unsolvability of the quintic equation in terms of radicals.

Math and the Mona Lisa, by Bűlent Atalay. Reviewed by Frank J. Swetz

The author makes the case for Leonardo da Vinci as the first modern scientist, as he discusses Leonardo's mathematics and science.

Pascal's Arithmetical Triangle, by A. W. F. Edwards. Reviewed by Richard M. Davitt

A history of the development of Pascal's triangle in its various manifestations.

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