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Society Investigating Mathematical Mind-Expanding Recreations

SIMMER at a glance
(for the 1999-2000 school year, with the most recent at the top)
For a more complete set of notes, see the ARCHIVES 

Topic: "Problems and Puzzles in Babylonian Mathematics"
Speaker: Prof. Craig G. Fraser (IHPST, University of Toronto)

The ancient Babylonians (ca. 1800 B.C.) possessed a sophisticated mathematics based on a positional base-sixty number system. Records of their mathematical achievements are found on clay tablets first unearthed by European archaeologists in the nineteenth century. Among other achievements the Babylonians were able to solve what we would today call quadratic equations and possessed rules for generating Pythagorean triplets of numbers.

The lecture provided an overview of Babylonian mathematics and then considered, among other things, the methods that the Babylonians used to obtain approximations to the square root of 2. Facsimiles of original Babylonian tablets were circulated and sample problems from their texts were posed as challenges for the audience to solve.

Here are some notes, references, sample problems and solutions.

The door prize, "A Concise History of Mathematics" written by Struik, was won by Nahid Golafsani.

Problems to think about for the November 1999 SIMMER meeting
Additional problems to think about, handed out at the November 1999 SIMMER meeting

Which triangular numbers are also squares? For which Pythagorean triples do the smallest numbers differ by 1? These and similar problems lead to a type of diophantine equation known as Pell's equation: x^2 - dy^2 = k, where d and k are given integers and we want solutions in positive integers x and y.

This equation has a long history that goes back to sixth-century India, and over the past four hundred years, European mathematics have studied it, eventually developing a coherent theory that can be extended to certain diophantine equations of higher degree.

We will look at the theory of this equation and some of its higher degree analogues. In preparation, you might try to get positive solutions in the special cases when d is between 2 and 100 inclusive, and k takes the values, 1, -1 and 4. In the case of 4, for which values of d are there solutions in odd integers?

The door prize, Ed Barbeau's book called "After Math", was won by Lesley Mason. Congratulations Lesley!

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This page was last updated: May 08, 2000