< 1 2 3 4 5 6 7 8 9 10 11 12 >
Pascal's triangle
In Pascal's triangle, the Fibonacci numbers are diagonals, that run upward.
Explanation
The Fibonacci sequence starts here with 1 because 0 does not make sense
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...
A number from this row is the sum of the numbers the run upward. This is indicated with different colours.
1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1 1 9 36 84 126 126 84 36 9 1 1 10 45 120 210 252 210 120 45 10 1
The calculation of the Fibonacci numbers in Pascal's triangle and in the Fibonacci sequence is by adding terms together.
Pascal's triangle Fibonacci sequence 1 = 1 1 = 1 2 = 1+1 = 1+1 3 = 1+2 = 1+2 5 = 1+3+1 = 2+3 8 = 1+4+3 = 3+5 13 = 1+5+6+1 = 5+8 21 = 1+6+10+4 = 8+13 34 = 1+7+15+10+1 = 13+21 55 = 1+8+21+20+5 = 21+34 89 = 1+9+28+35+15+1 = 34+55