The Fibonacci Sequence aka Fibonacci Numbers
In college, we have studied Fibonacci sequence in Algebra, Number Theory, Calculus and other subjects. However, Fibonacci sequence has been dealt with more focus in Number Theory – a field of mathematics dealing with the study of numbers, sequences, number patterns and theories regarding the development of numbers and equations.
According to wikipedia, 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 following recurrence relation:
- Fibonacci Sequence, Fibonacci Numbers
That is, after two starting values, each number is the sum of the two preceding numbers. The first Fibonacci numbers (sequence A000045 in OEIS), also denoted as Fn, for n = 0, 1, 2, … ,20 are:
-
F0 F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12 F13 F14 F15 F16 F17 F18 F19 F20 0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765
Every 3rd number of the sequence is even and more generally, every kth number of the sequence is a multiple of Fk.
The sequence extended to negative index n satisfies Fn = Fn?1 + Fn?2 for all integers n, and F?n = (?1)n+1Fn:
.., ?8, 5, ?3, 2, ?1, 1, followed by the sequence above.
Mathematics is all about spotting patterns, finding the underlying logic in the seemingly random and chaotic world around us; and using this information to predict future behaviour. Traditionally maths has been used to make predictions about inanimate objects, like the orbit of planets or the weather. But as Stephen Baker explains in The Numerati, mathematicians are increasingly turning their attention to human behaviour. What if those strings of numbers are records of the things you’ve bought, places you’ve travelled to, websites you’ve visited, parties you’ve voted for? Find the pattern in the numbers and mathematicians will be able to predict – with surprising accuracy – what your next move will be. The ‘numerati’ is the name Baker gives to the group of latterday fortune-tellers whose job it is to decode our behaviour. His book explores the lives of such people and attempts to analyse how powerful they have become…
Related posts
(No Ratings Yet)
Loading ...
