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Fibonaccia Introduction1 About Fibonacci1 Time period Hog 12 Fibonacci s Life Hog 1 Vaj 93 The Liber Abaci 2 The Fibonacci Sequence1 When discovered Vaj 72 Where it appears Vaj 93 The Golden Ratio1 When discovered2 Where it appears4 Thesis The Fibonacci Sequence and The Golden Ratio are very much a part of one another and these two phenomena have many applications in math and nature b The Simple explanations1 How we arrive at the Fibonacci Sequence1 Explained in English2 Formula2 The Simplest Properties of the Fibonacci Numbers1 u1u2unun2-1 Vor 62 The sum of Fodd u1u3u5u2n-1u2n Vor 73 Sum of Feven u2u4u2nu2n1-1 Vor 74 u12u22un2unun1Vor 83 How we arrive at the Golden Ratio1 Explanation of it 1 Explanation of Golden Rectangle2 Formula to get it - Solve for X with a formula and Diagram3 How to get from Fibonacci series to Golden Ratio 4 Properties of the Golden Ratio1 a 2a1 Hog 92 1a a -13 b 2b 1c Fibonacci Numbers1 In Math2 In Natured The Golden Ratio1 In Math2 In Naturee ConclusionOne would be hard pressed to name any significant mathematicians from the middle ages the thirteenth century Indeed they were few and far between The solitary light during this dark age of mathematical and scientific void was Leonardo Fibonacci also known as Leonardo of Pisa Hog 1 During his lifetime c 1170 1250 Fibonacci produced one great work the Liber Abaci Vaj 9 The title of this work which was written in 1202 literally means a book about the abacus Vor 1 It is an excessively comprehensive work encompassing nearly all the arithmetic and algebraic knowledge of the time This book played an important role in the evolution of Western European mathematics but in particular it familiarized the Europeans with the Hindu or Arabic numerals 1 Although his book spoke of many different topics Fibonacci is most known for the sequence of numbers1 1 2 3 5 8 13 21 34 55 to
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