# Convergence articles

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The annual meeting of the NCTM always contains sessions dealing with the history of mathematics and its use in teaching.

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

Page 8, Images from the Paul Halmos Photograph Collection: Armand Borel, Karol Borsuk, Raoul Bott, William Browder, H. Arlen Brown, and R. Creighton Buck

A new history of mathematics text which asks lots of questions about the history and the mathematics.

This is the title page of the Treatise of Algebra (1685), by John Wallis. This is probably the first attempt at a history of the subject of algebra, presented in the context of a text on the subject. Among the most famous parts of this treatise is Wallis's discussion of the work of Thomas Harriot, especially his contention that Rene Descartes plagiarized Harriot's symbolization procedure in algebra.

If an arc of 45 degrees on one circumference is equal to an arc of 60 degrees on another circle, what is the ratio of the areas of the circles?

Two bicyclists travel in opposite directions around a quarter-mile track and meet every 22 seconds. When they travel in the same direction on this track, the faster passes the slower once every 3 minutes and 40 seconds. Find the rate of each rider

A man entered an orchard through 7 gates, and there took a certain number of apples. When he left the orchard, he gave the first guard half the apples he had and 1 apple more.

In Archimedes' Book of Lemmas (ca 250), he introduces a figure that, due to its shape, has historically been known as "the shoemaker's knife" or arbelos.

One person possesses 7 asava horses, another 9 haya horses, and another 9 camels. Each gives two animals away, one to each of the others.