FIBONACCI SEQUENCE 1.pdf
- 1. FIBONACCI SEQUENCE What is the Fibonacci sequence? The Fibonacci sequence is a set of integers (the Fibonacci numbers) that starts with a zero, followed by a one, then by another one, and then by a series of steadily increasing numbers. The sequence follows the rule that each number is equal to the sum of the preceding two numbers.
- 2. Fibonacci was born Leonardo Pisano Bigollo sometime in 1170 A.D. The exact date of his birth is not known. He was born into privilege as his father was a well- to- do merchant. His father did a great deal of work in North Africa and young Fibonacci would travel with him. The travels exposed the young man to the Hindu–Arabic numeral system that he later brought to Europe. Fibonacci is considered by historians to be among the greatest of all mathematicians during that time period. The Hindu–Arabic numeral system was able to be spread throughout Europe.
- 3. The Fibonacci Sequence is the series of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, … The next number is found by adding up the two numbers before it. The 2 is found by adding the two numbers before it (1+1) The 3 is found by adding the two numbers before it (1+2), And 5 is (2+3), and so on! Example: the next number in the sequence above is 21+34 = 55
- 4. . The Rule: The Fibonacci Sequence can be written as a “Rule” First, the terms are numbered from 0 onwards like this: Fn = F0, F1, F2, F3, F4, F5, F6,…… 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, .. The Fibonacci sequence begins with the following of integers:
- 5. F0 = 0 F10 = 55 F1 = 1 F11 = 89 F2 = 1 F12 = 144 F3 = 2 F13 = 233 F4 = 3 F14 = 377 F5 = 5 F15 = 610 F6 = 8 F16 = 987 F7 = 13 F17 = 1597 F8 = 21 F18 = 2584 F9 = 34 F19 = 4181 Fibonacci Numbers List Using the Fibonacci numbers formula and the method to find the successive terms in the sequence formed by Fibonacci numbers, explained in the previous section, we can form the Fibonacci numbers list as shown below.
- 6. Makes A Spiral When we make squares with those widths, we get a nice spiral: