Golden Ratio and Fibonacci Series

Introduction The Fibonacci Series The Fibonacci Series is a sequence of numbers first created by Leonardo Fibonacci (fibo-na-chee) in 1202. It is a deceptively simple serial publication, but its ramifications and applications are nearly limitless. It has fascinated and stupefy mathematicians for over 700 years, and nearly everyone who has worked with it has added a new piece to the Fibonacci puzzle, a new tidbit of information slightly the series and how it works. Fibonacci mathematics is a constantly expanding branch of number theory, with more and more people being Yellow flower with 8 petals, a Fibonacci rawn into the complex subtleties of Number. Fibonaccis legacy. The first two numbers in the series are one and one. To obtain each number of the series, you simply add the two numbers that came in advance it. In other words, each number of the series is the sum of the two numbers preceding it. punctuate Historically, some mathematicians have considered zero to be a Fibonacci number, placing it before the first 1 in the series. It is cognize 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. html Series (0,) 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 EXAMPLE IN spirit Fibonacci SeriesActivity 1 Using a piece of graph paper, draw a loop using the Fibonacci series. Starting in the center of the page, draw a 1 X 1 square, neighboring to it draw another 1 X 1 square, After, draw 2 X 2 squares touch modality the last two squares, Then continue to add on squares until the graph paper is filled. To finish the helix draw arcs (quarter circles) in each square starting in the center and working outward. Do you mailing any similarity to the spiral you have drawn and the image of the shell?Fibonacci SeriesActivity 2 Take the Fibonacci sequence listed below and give each pair of number and record the results 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 universe around us and (as you saw) is related to the Fibonacci series. Fibonacci SeriesActivity 3 each(prenominal) hand has how many digits? _______________ each(prenominal) flip 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 length 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 medium length, what do you get? ________________ Now divide the medium length by the shortest length, what do you get t his time? ___________ What is the ratio? ____________________________________