One of the most compelling Number Patterns in Mathematics is The Pascal's Triangle which is named after Blaise Pascal, a famous French Mathematician and Philosopher. To build the triangle, start with "1" at the top, then continue placing numbers below it in a triangular pattern.
Each number is just the two numbers above it added together.
The Binomial Theorem is a quick way of multiply out a binomial expression that has been raised to some (generally inconveniently large) power. For instance, the expression
(6x + 1)^6 would be very painful to multiply out by hand. By applying the binomial expansion with coefficients from the Pascal’s triangle, it is easier to arrive at the solution quite quickly.
There are other very interesting facts about the Pascal's triangle.