[pic02] A tiling with squares whose sides are successive Fibonacci numbers in length
[pic03] A Fibonacci spiral created by drawing arcs connecting the opposite corners of squares in the Fibonacci tiling; this one uses squares of sizes 1, 1, 2, 3, 5, 8, 13, 21, and 34; see Golden spiral
節錄自wikipedia
斐波那契數列（Fibonacci Sequence），台灣譯為費氏數列。
在數學上，斐波那契數列是以遞歸的方法來定義：
F0 = 0
F1 = 1
Fn = (Fn - 1) + (Fn - 2)
用文字來說，就是斐波那契數列由0和1開始，之後的斐波那契數就由之前的兩數相加。首幾個斐波那契數是（OEIS A000045）：
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946，………………
特別指出：0不是第一項，而是第零項。
In mathematics, the Fibonacci numbers are a sequence of numbers named after Leonardo of Pisa, known as Fibonacci. Fibonacci's 1202 book Liber Abaci introduced the sequence to Western European mathematics, although the sequence had been previously described in Indian mathematics.
The first number of the sequence is 0, the second number is 1, and each subsequent number is equal to the sum of the previous two numbers of the sequence itself, yielding the sequence 0, 1, 1, 2, 3, 5, 8, etc. In mathematical terms, it is defined by the [pic01] recurrence relation:
That is, after two starting values, each number is the sum of the two preceding numbers. The first Fibonacci numbers also denoted as Fn, for n = 0, 1, 2, … ,20 are:
[F0]0, [F1]1, [F2]1, [F3]2, [F4]3, [F5]5, [F6]8, [F7]13, [F8]21, [F9]34, [F10]55, [F11]89, [F12]144, [F13]233, [F14]377, [F15]610, [F16]987, [F17]1597, [F18]2584, [F19]4181, [F20]6765
沒有留言:
張貼留言