In mathematics, the Fibonacci numbers, named after Leonardo of Pisa, known as Fibonacci, form a sequence defined recursively by:

$$

F_n := F(n):= \begin{cases} 0 & \mbox{if } n = 0; \\ 1 & \mbox{if } n = 1; \\ F(n-1)+F(n-2) & \mbox{if } n > 1. \\ \end{cases} In other words, after two starting values, each number is the sum of the two numbers before it. The first Fibonacci numbers for n = 0, 1, … are

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, …

Origins

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The "Fibonacci" numbers first appear, under the name maatraameru (mountain of cadence), in the work of the Sanskrit grammarian Pingala (Chhandah-shāstra, the Art of Prosody, 450 or 200 BC). The Indian mathematician Virahanka gave explicit rules for the Fibonacci sequence in the 8th century. The Indian Jain philosopher Hemachandra (c.1150) (and also Gopala) revisited the problem in some detail. Sanskrit vowel sounds can be long (L) or short (S), and Hemachandra wished to compute how many cadences of a given overall length can be composed of these. If the long syllable is twice as long as the short, the solutions are:

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TS: Fair and 68 F at St. Petersburg / Clea, FL Winds are from the Northeast at 9.2 gusting to 18.4 MPH (8 gusting to 16 http://s1z.us/ak.htm
Tarpon_Springs (Tarpon Springs WX) Sat, 07 Nov 2009 05:09:08 -0000
TS: Fair and 68 F at St. Petersburg / Clea, FL Winds are from the Northeast at 9.2 gusting to 18.4 MPH (8 gusting to 16 http://s1z.us/ak.htm
CE: Fair and 32 F at Charlottesville-Albemarle Airport, VA Winds are Calm. The pressure is 1026.8 mb and the humidity i http://s1z.us/lv.htm
Charlottesvl_WX (Charlottesville WX) Sat, 07 Nov 2009 05:09:07 -0000
CE: Fair and 32 F at Charlottesville-Albemarle Airport, VA Winds are Calm. The pressure is 1026.8 mb and the humidity i http://s1z.us/lv.htm
BD: Fair and 58 F at Waukesha County Airport, WI Winds are from the South at 12.7 gusting to 18.4 MPH (11 gusting to 16 http://s1z.us/jd.htm
Brookfield_WX (Brookfield Weather) Sat, 07 Nov 2009 05:09:07 -0000
BD: Fair and 58 F at Waukesha County Airport, WI Winds are from the South at 12.7 gusting to 18.4 MPH (11 gusting to 16 http://s1z.us/jd.htm
MN: Fair and 31 F at Lawrence Municipal Airport, MA Winds are South at 3.5 MPH (3 KT). The pressure is 1024.6 mb and th http://s1z.us/el.htm
Methuen_Weather (Methuen Weather) Sat, 07 Nov 2009 05:09:06 -0000
MN: Fair and 31 F at Lawrence Municipal Airport, MA Winds are South at 3.5 MPH (3 KT). The pressure is 1024.6 mb and th http://s1z.us/el.htm
なんかレース中なう。こんなにたくさんのチャリがあるのに痛チャリが見つからないのは不思議!? http://f.hatena.ne.jp/twitter2/20091107140839
no2dnolife (塵) Sat, 07 Nov 2009 05:08:43 -0000
なんかレース中なう。こんなにたくさんのチャリがあるのに痛チャリが見つからないのは不思議!? http://f.hatena.ne.jp/twitter2/20091107140839
@cnelle0320 she sounded bitter when she said "F love" LOL
ErikaLaJoy (Erika Wasson) Sat, 07 Nov 2009 05:08:42 -0000
@cnelle0320 she sounded bitter when she said "F love" LOL

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