Continuing this you will find that Bob has eight great-great-great grandparents, thirteen great-great-great-great grandparents, and so on. There is even a simple algorithm for finding this representation: just use the greedy algorithm, always picking the largest Fibonacci number that will still ‘fit’. So Bob has a total of five great-great grandparents. In fact every positive integer can be written uniquely as a sum of one or more non-consecutive Fibonacci numbers this is known a Zeckendorf’s theorem. One of those will be male and therefore have one parent, while the other two are female and therefore have a total of four parents. His grandfather will only have one parent, while his grandmother will have two, so in total Bob has three great-grandparents. This means that Bob has two grandparents. Bob (the male symbol at the bottom of the tree, a circle with above an arrow) has one parent (the queen bee – represented by the female symbol, a circle above a cross) who herself has two parents (since she comes from a fertilised egg). The petals unfold more and more and the sequence increases. I like it because the petals arent spread out and the spiral is more obvious and clear, like with the shell. Now let's look at the family tree of a male bee called Bob. Flowers of all kinds follow the pattern, but roses are my favorite kind to use as an example of the Fibonacci Sequence. If an egg is fertilised by a male bee, then the egg produces a female worker bee, who doesn't lay any eggs herself. If an egg is not fertilised it eventually hatches into a male bee, called a drone. The following is a full list of the first 10, 100, and 300. The sequence formed by Fibonacci numbers is called the Fibonacci sequence. That is F n F n-1 + F n-2, where F 0 0, F 1 1, and n2. Whether we realize it or not, we can see patterns around us all the time: in math, art, and other areas of life. In mathematics, the Fibonacci numbers form a sequence such that each number is the sum of the two preceding numbers, starting from 0 and 1. In every bee hive there is one female queen bee who lays all the eggs. The Fibonacci sequence is a series of numbers developed by Leonardo Fibonacci a mathematician who was inspired by the patterns he found in nature and the everyday world. The Fibonacci sequence – 1, 1, 2, 3, 5, 8.
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