Pascal's Triangle

Beauty in Mathematics

Fibonacci sequence

Let us consider light switches

Relationship of different rows



Why does this relationship hold? Let's go back to the light switches.
Set one switch on or off. Then there are:


ways left to choose the rest.

Relationship to binomials


(a + b) = a + b
(a + b)2 = a2 +2ab + b2
(a + b)3 = a3 +3a2b + 3ab2 + b3
(a + b)4 = a4 +4a3b +6a2b2 + 4ab3 + 3b4



Relationship to the Fibonacci Sequence

Amazingly, the diagonals of the Pascal's Triangle sum to the members of the Fibonacci sequence!

External Links


Blaise Pascal