Golden Ratio and Fibonacci Series

Introduction The Fibonacci serial The Fibonacci serial is a sequence of numbers send-off created by da Vinci Fibonacci (fibo-na-chee) in 1202. It is a deceptively simple series, but its ramifications and applications are nigh limitless. It has fascinated and perplexed mathematicians for over 700 years, and nearly everyone who has worked with it has added a new natural selection to the Fibonacci puzzle, a new tidbit of information about the series and how it works. Fibonacci maths is a constantly expanding branch of number theory, with more and more state being Yellow flower with 8 petals, a Fibonacci rawn into the complex subtleties of Number. Fibonaccis legacy. The first ii numbers in the series are one and one. To set about distributively number of the series, you simply add the two numbers that came forward it. In other words, each number of the series is the sum of the two numbers preceding it. Note Historically, some mathematicians have realizeed zero to be a Fibona cci number, placing it before the first 1 in the series. It is known as the zeroth Fibonacci number, and has no real practical merit. We will not consider zero to be a Fibonacci number in our discussion of the series. http//library. thinkquest. rg/27890/mainIndex. hypertext markup language Series (0,) 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 EXAMPLE IN NATURE Fibonacci Series drill 1 Using a piece of chart paper, draw a spiral using the Fibonacci series. Starting in the center of the page, draw a 1 X 1 solid, next to it draw another 1 X 1 square, After, draw 2 X 2 squares contemptible the last two squares, Then continue to add on squares until the graph paper is filled. To finish the spiral draw arcs (quarter circles) in each square starting in the center and working outward. Do you observance whatsoever similarity to the spiral you have drawn and the image of the shell?Fibonacci SeriesActivity 2 Take the Fibonacci sequence listed below and divide each pair of number and record the res ults in the table. 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 combo results 1/1 2/1 3/2 5/3 8/5 13/8 21/13 34/21 55/34 89/55 What do you notice? This is called the golden ratio. (Phi is 161803398874 ) This is another special number that appears in the arena around us and (as you saw) is related to the Fibonacci series. Fibonacci SeriesActivity 3 distributively hand has how many digits? _______________ to each one finger has how many bones? _______________ Each finger has how many joints between the just inger bones themselves? _______________ Each finger has how many finger nails? What pattern do you see? _______________ _______________________________ Now pick one finger Measure the aloofness of each of the three segments this is the easiest to do if the finger is bent. Longest _______________cm Medium _______________cm Shortest _______________cm Now divide the longest length by the modal(a) length, what do you get? ________________ Now divide the medium length by the shortest leng th, what do you get this time? ___________ What is the ratio? ____________________________________