The mathematical secrets of Pascal’s triangle - Wajdi Mohamed Ratemi

This may look like a neatly arranged stack of numbers, but it's actually a mathematical treasure trove.

Indian mathematicians called it the Staircase of Mount Meru. In Iran, it's the Khayyam Triangle.

And in China, it's Yang Hui's Triangle. To much of the Western world, it's known as Pascal's Triangle

after French mathematician Blaise Pascal, which seems a bit unfair since he was clearly late to the party,

but he still had a lot to contribute. So what is it about this that has so intrigued mathematicians the world over?

In short, it's full of patterns and secrets. First and foremost, there's the pattern that generates it.

Start with one and imagine invisible zeros on either side of it. Add them together in pairs, and you'll generate the next row.

Now, do that again and again. Keep going and you'll wind up with something like this,

though really Pascal's Triangle goes on infinitely. Now, each row corresponds to what's called the coefficients of a binomial expansion

of the form (x+y)^n, where n is the number of the row,