Friday, November 6, 2009

Mathematicians Solve “Trillion Triangle” Problem

Through the extensive use of a modern computer hard drive, mathematicians gathered from four continents to perform calculations on a thousand-year old triangle problem. The problem involved numbers so large that if the digits were written by hand, they would stretch to the moon and back. The problem posed, dealt with areas of right-angled triangles. It involved determining which whole numbers could be the area of a right-angled triangle whose sides are whole numbers or fractions. The area of such a triangle is called a “congruent number.” The calculation found congruent number sequences up to a trillion. Team members involved in performing these calculations, developed a fast, general library of computer code to do the calculations. Once they did that, it didn’t take them long to write the specific program needed to for this particular calculation. The software is freely available, and anyone with a larger computer can use it to break this team’s record. They also found that previous predictions on how congruent numbers behave statistically were quite accurate.
Activities for the classroom: In math, we are always asking students to look for and extend patterns. They sometimes see how tedious this could be when written by hand. This article shows how modern-day technology can make these calculations much easier. We are also having students make generalizations about procedures in math to develop formulas and algorithms, and this article shows how the same process was successful for other mathematicians. We can also show them how to apply and write simple formulas that can be used to deal with large data sets/tedious computational tasks within Microsoft Excel.

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