{"id":6776,"date":"2014-03-11T16:34:04","date_gmt":"2014-03-11T16:34:04","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=6776"},"modified":"2014-12-02T08:25:31","modified_gmt":"2014-12-02T08:25:31","slug":"math-introduction-to-fibonacci-numbers","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/math-introduction-to-fibonacci-numbers\/","title":{"rendered":"Math Introduction to Fibonacci Numbers"},"content":{"rendered":"

Overview:<\/strong><\/p>\n

What does the spiral arrangement of leaves on a pine cone have in common with the arrangement of florets in a center of a daisy or the spirals of fruit buds on a pineapple?\u00a0 Those spirals can be approximated by a mathematical sequence of numbers known as Fibonacci numbers.<\/p>\n

What Is the Fibonacci Sequence?<\/strong><\/p>\n

The Fibonacci Sequence is a definite pattern that can begin with either 0, 1 or 1, 1.\u00a0 The sequence is generated by adding the previous terms, so that 0 +1 equals 1, 1+1 equals 2, 2 + 1 equals 3, 2 + 3 equals 5, 5 + 3 equals 8, 8 + 5 equals 13, 13 + 8 equals 21, 21 + 13 equals 34, 34 + 21 equals 55, and so on.\u00a0 In other words, the sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, and so on, infinitely.<\/p>\n

How Do Other Numbers Relate to the Fibonacci Sequence?<\/strong><\/p>\n

Not all numbers are Fibonacci numbers.\u00a0 However, they can be generated by adding Fibonacci numbers.\u00a0 For example, 4 is not a Fibonacci number, but it is the sum of two Fibonacci numbers, 3 + 1.\u00a0 Similarly, 10 is not a Fibonacci number, but it is the sum of 2 Fibonacci numbers, 8 + 2.\u00a0 Sometimes it takes more than 2 Fibonacci numbers.\u00a0 For example, 43 is the sum of 34 + 8 + 1. The number 95 is the sum of 89 + 3 + 1 + 2.<\/p>\n

What Is the Golden Ratio?<\/strong><\/p>\n

The Golden Ratio is a mathematical relationship that is closely related to the Fibonacci sequence.\u00a0 The ratio of the first two Fibonacci numbers 1\/1 is equal to 1, and the ratio of the second two, 2\/1 is equal to 1 + 1\/1.\u00a0 The ratio of the third, is 3\/2, or 1.5. The ratio of the fourth is 5\/3, or 1.66.\u00a0 No matter how many adjacent Fibonacci numbers are compared, the ratio of those numbers is very close to a number that the ancient Greek mathematicians called phi (\u03c6).\u00a0 The number phi has several connections with classical proportions in art, geometry, and architecture.<\/p>\n

What Are Other Applications of Fibonacci Numbers?<\/strong><\/p>\n

Fibonacci numbers are also used in applications of computer algorithms.\u00a0 They can be used to compress audio files and generate code.\u00a0 They permeate art, music, and literature.\u00a0 Most recently, Fibonacci numbers have been used to symbolize mathematical relationships in The DaVinci Code<\/i>, as well as in the TV shows Fringe, Criminal Minds, <\/i>and Taken.<\/i><\/p>\n

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Overview: What does the spiral arrangement of leaves on a pine cone have in common with the arrangement of florets in a center of a daisy or the spirals of fruit buds on a pineapple?\u00a0 Those spirals can be approximated by a mathematical sequence of numbers known as Fibonacci numbers. What Is the Fibonacci Sequence? […]<\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2],"tags":[2624,2625],"class_list":["post-6776","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-fibonacci-number-sequence","tag-golden-ratio"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6776","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=6776"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6776\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=6776"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=6776"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=6776"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}