Question

The Fibonacci sequence appears in the book Liber Abaci (1202) by Fibonacci. Fibonacci considered the growth of an idealized (biologically unrealistic) rabbit population, assuming that: a newly born pair of rabbits, one male, one female, are put in a field; rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits; rabbits never die and a mating pair always produces one new pair (one male, one female) every month from the second month on. The puzzle that Fibonacci posed was: how many pairs will there be in one year? Explain why your seript is answering Fibonad's puzle According to wikipedia: Fibonacci numbers appear unexpectedly often in mathematics, so much so that there is an entire journal dedicated to their study, the Fibonacci Quarterly Applications of Fibonacci numbers include computer algorithms such as the Fibonacci search technique and the Fibonacci heap data structure, and graphs called Fibonacci cubes used for interconnecting parallel and distributed systems. They also appear in biological settings, such as branching in trees, the arrangement of leaves on a stem, the fruit sprouts of a pineapple, the flowering of an artichoke, an uncurling fern and the arrangement of a pine cone's bracts. Although named after an Italian mathematician, the sequence had been described earlier in Indian mathematics. More from wikipedia: The Fibonacci sequence appears in Indian mathematics in connection with Sanskrit prosody In the Sanskrit poetic tradition, there was interest in enumerating all patterns of long (L) syllables of 2 units duration, juxtaposed with short (S) syllables of 1 unit duration. Counting the different patterns of successive L and S with a given total duration results in the Fibonacci numbers: the number of patterns f duration m units is Fm+1 sequence was also expressed as early as Pingala (c. 450 BC-200 Knowledge of the Fibonacci Singh cites Pingala's cryptic formula misrau cha ("the two are mixed") and scholars BC). saying that the number of patterns for m beats (Fmrt) is who interpret it in context as ed by adding one [S to the Fm cases and one [L] to the Fmi cases.

*** PLease answer all questions to ur best ability. Thank you! if you do ill give good rating. the language is python.

Answer 1

There appears to be only one question, rest is facts about Fibonacci sequences, indeed an important and extremely used sequence. Let us see what the question wants to convey.

It says that we started with one pair of rabbits, we produce another pair of rabbits in one month.

If you carefully read the question you will know a pair of rabbits can produce offsprings after they have grown up (stated as, a pair of rabbits can produce offsprings whey are a month old, i.e at the end of second month the female rabbit can produce a pair)

Suppose we take the initial pair of rabbits to be born on January 1.

on February 1, they do not reproduce because they are not grown up yet, so on Feb 1 also there is only one pair.

on March 1, the first pair can produce a pair of rabbits and so we have 2 pairs now.

on April 1, the original pair produces one more pair and the pair born on march 1, just grows up and does not produce an offspring. So we have 3 pairs.

on May 1 we have the original pair, one grown up pair born on March 1 and the new born pair born on April 1. So now the two grown up pair produces two new pairs . In total we have 5 pairs. (3 grown and two new born).

if you start to observe carefully we are using a Fibonacci sequence. A Fibonacci sequence is defined as series in which every number of the series is a sum of the two previous numbers.

i.e. $F_n = f_{n-1} + f_{n-2} \: \: \: \forall \: \: n \geq 2$ where $F_n$ denotes fibonacci number.

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Month NamePairs January 1 February 1 March 1 1+1 2 April 1 2+1 = 3 May 1 3+2-5 June 1 5+3-8 8+5-13 July 1 13+8-21 August 1 September 1 21+13-34 October 1 21+34 55 2 3 November 1 55+34-89 0 55+89-144 December 1

If you go on counting you will find out by the end of 12 months we will have 144 pairs.

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