<    1      2      3    >

---

Fibonacci numbers

The Fibonacci numbers form diagonals in Pascal's triangle, where they go right up.

 

---

Explanation

The sequence starts here with 1 because 0 doesn't make sense

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...

A number arises from the sum of the numbers diagonally upwards to the right.

1 →	1
1 →	1	1
2 →	1	2	1
3 →	1	3	3	1
5 →	1	4	6	4	1
8 →	1	5	10	10	5	1
13 →	1	6	15	20	15	6	1
21 →	1	7	21	35	35	21	7	1
34 →	1	8	28	56	70	56	28	8	1
55 →	1	9	36	84	126	126	84	36	9	1
89 →	1	10	45	120	210	252	210	120	45	10	1

The calculation of the Fibonacci numbers in the Pascal triangle and in the Fibonacci sequence is done 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

 

---

History Fibonacci (1180 - 1241), described it after examining fast-growing populations in the animal world.

---

Deutsch   Español   Français   Nederlands   中文   Русский