Write a recursive formula for the fibonacci sequence in nature
They are called complex numbers and have two parts A and B, both normal real numbers: a real part, A, and an imaginary part, B. Now let's look at another reasonably natural situation where the same sequence "mysteriously" pops up.
I haven't yet found an explanation for this - can you find one? Electrical engineers tend to use j rather than i when writing complex numbers.
Fibonacci spiral explained
Note how this curve crosses the x axis representing the "real part of the complex number" at the Fibonacci numbers, 0, 1, 2, 3, 5 and 8. I haven't yet found an explanation for this - can you find one? But what Fibonacci could not have foreseen was the myriad of applications that these numbers and this method would eventually have. Consider an elementary example of geometric growth - asexual reproduction, like that of the amoeba. The Zeckendorf representation of a number can be used to derive its Fibonacci coding. A one-dimensional optimization method, called the Fibonacci search technique , uses Fibonacci numbers. You can see from the tree that bee society is female dominated. Instead of going from n down to lower values, we can make a loop that starts from 1 and 2, then gets fib 3 as their sum, then fib 4 as the sum of two previous values, then fib 5 and goes up and up, till it gets to the needed value. The function should be fast. Now it looks as if the two curves are made from the same 3-dimensional spiral spring-shape, a bit like the spiral bed-springs in cartoons, getting narrower towards one end. This pattern turned out to have an interest and importance far beyond what its creator imagined.
So, one amoebas becomes two, two become 4, then 8, 16, 32, and so on. The story began in Pisa, Italy in the year So this sequence of numbers 1,1,2,3,5,8,13,21, Five end with a long syllable and eight end with a short syllable.
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