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Fibonacci Sequence 0, 1 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 … = 10, = 20, 1, = 3 0, 1, 1, = 50, 1, 1, 2, = 8
Golden Ratio 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 …
Golden Spiral 1x1 2 x 2 3 x 3 5 x 5 8 x 8 13 x x 21
Golden Ratio Found in Nature
Flowers Petals: Seeds:
Animals Fibonacci Rabbits: Ideal Reproductive HabitsPhysical Structure
The Physical World
The Human Body
The Human Figure
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The search for good information To help you guide investments.
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Petals Most flowers have 5 or 8 petals Seeds Many plants have 3, 5 or 8 seeds.
Homework – Chapter 1 作業解答. Problem 1 Given the Fibonacci number as … where the next Fibonacci number will be the sum of its previous.
1 Excursions in Modern Mathematics Sixth Edition Peter Tannenbaum.
Digital Design: Fibonacci and the Golden Ratio. Leonardo Fibonacci aka Leonardo of Pisa 1170 – c
2, 5, 8, 11,... 1, 4, 9, 16,... 9, 8, 6, 3,... 1, 1, 2, 3, 5, 8,... 14, 17, 20 25, 36, 49 -1, -6, , 21, 34.
Fibonacci Numbers By Anna Jean From The Grade 4 Class.
The Fibonacci Sequence. Leonardo Fibonacci (1170 – 1250) First from the West, but lots of evidence from before his time.
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By Steven Cornell. Was created by Leonardo Pisano Bogollo. It show’s the growth of an idealized rabbit population.
Tree Recursion Traditional Approach. Tree Recursion Consider the Fibonacci Number Sequence: Time: , 1, 1, 2, 3, 5, 8, 13, 21,... /
Introduction This project is about a great mathematician that made a chain of numbers that are called Fibonacci number chain. In this PowerPoint I will.
The Fibonacci sequence occurs throughout nature. Where does the Fibonacci sequence occur on the human body and in animals?
Φ. The golden ratio is a ratio that states if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity.
Math text books and math note books on your desks, please. Sharpened pencils Calculators if you have one Brain starter: Add up all the numbers.
1 Fibonacci Numbers Stage 4 Year 7 Press Ctrl-A ©2009 – Not to be sold/Free to use.
Mathematics and the Wonders of Creation by James Nickel B.A., B.Th., B.Miss., M.A. Copyright
THE BEAUTY AND REALITY OF MATHEMATICS. HEARTFELT THANKS TO THOSE BEFORE US……..WITH US NOW…………AND TO COME ALL THE GIFTS HAVE MADE LIFE BETTER.
The Fibonacci Sequence. These are the first 9 numbers in the Fibonacci sequence
Fibonacci Numbers By: Darrin Goldberg Sai Palati Alaina Lynch Allan Fridlikh.
BEAUTY PHI BEHOLDER of the is in the. Beauty A quality that gives aesthetic pleasure Visual pleasantness of a person, animal, object or scene. Pleasantness.
Fibonacci numbers Month 0 1 pair Month 1 1 pair Month 2 2 pairs Month 3 3 pairs 10 February, 2014 Jenny Gage University of Cambridge.
Mathematics and God God is Creator God is the Creator of everything, and he uses maths in the things that he makes. Not just that,
TWO STEP EQUATIONS 1. SOLVE FOR X 3. DIVIDE BY THE NUMBER IN FRONT OF THE VARIABLE 2. DO THE ADDITION STEP FIRST.
1 Chapter 1 The Study of Body Function Image PowerPoint Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
WEEK 1 You have 10 seconds to name…
GOLDEN RATIO GOLDEN SECTION FIBONACCI NUMBERS 1, 1, 2, 3, 5, 8, 13….. The ratio of any consecutive numbers is the golden ratio A pattern found in nature.
Fibonacci Numbers and Binet Formula (An Introduction to Number Theory) By: (The Ladies) 2.
Fibonacci Sequences and the Golden Ratio Carl Wozniak Northern Michigan University.
Fibonacci Born in: Pisa in 1175 Nickname: Fibonacci Real name: Leonardo Pisano or Leonardo of Pisa.
Recursive Sequences Terry Anderson. What is a Recursive Sequence? A sequence that follows a pattern involving previous terms To generate new terms,
The Fibonacci Sequence The sequence of numbers 1,1,2,3,5,8….in which each successive number is equal to the sum of the two preceding numbers.
MATH 2160 Sequences. Arithmetic Sequences The difference between any two consecutive terms is always the same. Examples: 1, 2, 3, … 1, 3, 5, 7, … 5, 10,
BY: MARK WEIMER APOLLO TECHNOLOGY EDUCATION Photography & Math…. huh?
Copyright © 2012, Elsevier Inc. All rights Reserved. 1 Chapter 7 Modeling Structure with Blocks.
Year 6 mental test 15 second questions Calculation Addition.
Problem-Solving Strategy: Look for a pattern Objective: Solve problems by looking for a pattern.
Proportions Section 6-1. ratio – a comparison of 2 quantities The ratio of a to b can be expressed as a:b or where b is not 0.
1 1. Fibonacci Sequence 2. Golden ratio Lecture 4.
MATHS IN NATURE AND ARTS FIBONACCI’S SEQUENCE AND GOLDEN RATIO.
Step 1 Number the first 25 lines on your paper, (1,2,3…)
©Brooks/Cole, 2001 Chapter 12 Derived Types-- Enumerated, Structure and Union.
Beautiful Nature Nature.
Golden Ratio Aka Golden rectangle, Divine ratio. Beautiful?
Chapter 13 Fluids Physics for Scientists & Engineers, 3 rd Edition Douglas C. Giancoli © Prentice Hall.
Liang, Introduction to Java Programming, Eighth Edition, (c) 2011 Pearson Education, Inc. All rights reserved Chapter 20 Recursion.
Results: Tables and Figures. Tables and Figures When to use what? Text: for simple results E.g. Seed production was higher for plants in the full-sun.
Types of Number. Prime Numbers Prime numbers are numbers that only divide by themselves and 1 1 is not a prime number because it can only be divided by.
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