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The Fibonacci sequence is frequently referenced in the 2001 book The Perfect Spiral by Jason S. Hornsby. A youthful Fibonacci is one of the main characters in the novel Crusade in Jeans (1973). He was left out of the 2006 movie version, however. The Fibonacci sequence and golden ratio are briefly described in John Fowles's 1985 novel A Maggot.
All these sequences may be viewed as generalizations of the Fibonacci sequence. In particular, Binet's formula may be generalized to any sequence that is a solution of a homogeneous linear difference equation with constant coefficients. Some specific examples that are close, in some sense, to the Fibonacci sequence include:
Another example in this chapter involves the growth of a population of rabbits, where the solution requires generating a numerical sequence. [8] Although the problem dates back long before Leonardo, its inclusion in his book is why the Fibonacci sequence is named after him today.
According to author Leon Harkleroad, "Some of the most misguided attempts to link music and mathematics have involved Fibonacci numbers and the related golden ratio." [61] With few exceptions, numerators for the meter signatures (over 100) in Karlheinz Stockhausen's Klavierstück IX are either Fibonacci or Lucas numbers. [62]
A repfigit, or Keith number, is an integer such that, when its digits start a Fibonacci sequence with that number of digits, the original number is eventually reached. An example is 47, because the Fibonacci sequence starting with 4 and 7 (4, 7, 11, 18, 29, 47) reaches 47. A repfigit can be a tribonacci sequence if there are 3 digits in the ...
In 1202, Leonardo Fibonacci introduced the Fibonacci sequence to the western world with his book Liber Abaci. [5] Fibonacci presented a thought experiment on the growth of an idealized rabbit population. [6] Johannes Kepler (1571–1630) pointed out the presence of the Fibonacci sequence in nature, using it to explain the pentagonal form of ...
Read no further until you really want some clues or you've completely given up and want the answers ASAP. Get ready for all of today's NYT 'Connections’ hints and answers for #583 on Tuesday ...
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