The Beauty of Pascal’s triangle


A Drawing of Pascal's triangle.

Benjamin Angell, Staff Writer

Pascal’s triangle is a triangle of numbers formed by a simple sum rule. To get the numbers in the next row, you add the two numbers directly above it. The Western world attributes Pascal’s triangle to Blaise Pascal, a French mathematician. However, this triangle was discovered long before that in Asia. Some cultures even named the triangle after people or objects that were significant to their culture, such as the “Staircase of Mount Meru” and the “Khayyam triangle”.

Although it is calculated with basic math, Pascal’s triangle has a variety of patterns and uses. Its most practical use is its role in combinatorics, but the triangle has other secrets. For example, if you count each row as a base-ten number it turns out that the rows are powers of eleven. Although Pascal’s triangle has practical uses, it also hides a host of patterns that have no practical uses but link to complex ideas. One of these patterns is in the third diagonal row. Those numbers are considered triangular numbers. Triangular numbers dictate how many units fit in each row of a triangle if you are starting with one unit. To many people, this is what makes the triangle so glamorous. Mr. Nestor, a Falmouth Academy math teacher, puts it nicely, “It’s just a basic thing, and the way it connects to so many complex mathematical ideas I just think is so interesting, and I think that’s why I always loved math.”