Fibonacci

Take a line (A) and divide it so that the ratio of the larger piece (B) to the whole line (A) is the same as the ratio as the small piece (C) to the larger piece (B): In the 12th century, Leonardo Fibonacci discovered an incredible mathematical relationship behind this seemingly simple proportion. It's based on a simple series of numbers, with each new number being the sum of the two before it. The Greeks knew this as the Golden Section. The Renaissance artists knew this as the Divine Proportion. Both used it for beauty and balance in the design of architecture. # Fibonacci Series With only one object, the total possible arrangments is limited to one, computed as 1 x 1. Two objects can be arranged two ways, computed as 2 x 1. If you were asked to guess the proper sequence for three objects, computed as 3 x 2 x 1, you would only have a one in six chance of getting it right. The total number of ways that any group of N objects can be arranged is: ```js:title=gatsby-config.js N x (N-1) x (N-2) x . . . x 1 ``` 1 object can be arraged in 1 way 2 objects can be arranged in 2 ways (i.e., 2 x 1) 3 objects can be arranged in 6 ways (i.e., 3 x 2 x 1) 4 objects can be arranged in 24 ways (i.e., 4 x 3 x 2 x 1) 5 objects can be arranged in 120 ways (i.e., 5 x 4 x 3 x 2 x 1) 6 objects can be arranged in 720 ways (i.e., 6 x 5 x 4 x 3 x 2 x 1) 7 objects can be arranged in 5,040 ways (i.e., 7 x 6 x 5 x 4 x 3 x 2 x 1) 8 objects can be arranged in 40,320 ways (i.e., 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) 9 objects can be arranged in 362,880 ways (i.e., 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) 10 objects can be arranged in 3,362,880 ways (i.e., 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) # Foundations of the Fibonacci Series 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, . . . 0, 1, 1, 2, 6, 120, 720, It is this simple series of numbers discovered by Leonardo Fibonacci that defines the ratio of the Golden Section and Divine Proportion. But that is just the beginning of its mathematical curiosities and mysteries. The ratio of each successive pair of numbers in the series quickly converges on 1.61804. . . , as 3 divided by 2 is 1.666..., and 8 divided by 5 is 1.60, and so on. The Fibonacci number(1.61804...), often called phi or Ø, was described by Johannes Kepler (1571-1630) as one of the "two great treasures of geometry." The other is the Theorem of Pythagoras. Square phi and you get a number exactly 1 greater than phi, 2.61804...: Ø squared = Ø + 1 Divide phi into 1 and you get a number exactly 1 less than phi, 0.61804...: 1 / Ø = Ø - 1 Take the square root of 5, add 1 and then divide by 2, and you also get phi. ( square root of 5 + 1 ) / 2 = Ø Which can also be expressed all in fives as: 5 ^ .5 * .5 + .5 = Ø The DNA molecule, the program for all life, is based on the golden section. It measures 34 angstroms long by 21 angstroms wide for each full cycle of its double helix spiral. 34 and 21, of course, are numbers in the Fibonacci series and their ratio, 1.6190476 closely approximates phi, 1.6180339. ```js:title=gatsby-config.js module.exports = { plugins: [ "gatsby-theme-blog", // highlight-line "gatsby-theme-notes", ], } ``` This is another paragraph after the code block. ## This is a secondary heading ```jsx import React from "react" import { ThemeProvider } from "theme-ui" import theme from "./theme" export default props => ( <ThemeProvider theme={theme}>{props.children}</ThemeProvider> ) ```