Pascal`s Triangle

Pascal`s triangle is the pattern formed where every number is the sum of the two above it. It looks like this:

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

and so on...

It has loads of sequences in it!

• If you read each row as a number you get 1, 11, 121, 1331, 14641... These are increasing powers of 11.
• If you add the elements of each row you get 1. 2. 4. 8, 16... These are powers of 2.
• The first diagonal is all 1s. The second diagonal is the counting numbers 1, 2, 3, 4... The third diagonal is the triangle numbers. The fourth are known as tetrahedral numbers - they`re like a 3-d version of triangle numbers.
• The elements of each row represent the binomial coefficients.
• E.g. (a+b)²=(1)a²+2ab+(1)b² and (a+b)³=(1)a³+3a²b+3b²a+(1)b³
• The Fibonacci numbers are even hidden in there - can you find them?