Arithmetic Triangle

HISTORY

The notion of finding the number of combinations of k objects from n objects in total has been explored in India since the ninth century. Indeed, there are traces of it in the Meru Prastara written by Pingala in around 200 BC.

Between the fourteenth and the fifteenth centuries, al-Kashi, a mathematician from the Iranian city of Kashan, wrote The Key to Arithmetic. In this work he calls binomial coefficients “exponent elements”.

In his work Traité du Triangle Arithmétique, published in 1665, Pascal, Blaise (1654) defined the numbers in the “arithmetic triangle”, and so this triangle is also known as Pascal's triangle.

We should also note that the triangle was made popular by Tartaglia, Niccolo Fontana in 1556, and so Italians often refer to it as Tartaglia's triangle, even though Tartaglia...