Lesson-1-Part-I-and-II-Intro-History-of-the-Golden-Ratio-and-Fibonacci-Revised-122316.pdf - Introduction History of The Golden Ratio Fibonacci Numbers


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The Golden Ratio & Fibonacci Numbers Introduction & History of
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Natureglo’s eScience Copyright 2015 Revised 12/15/16 Permission is granted to reproduce this PowerPoint per one family household, per one teacher classroom and for the purchaser’s personal use only. Please visit and follow Natureglo’s eScience today! Follow Natureglo’s eScience on Facebook: Follow Natureglo’s eScience on Twitter: Follow NaturGlo’s eScience on Pinterest: You can connect with Natureglo’s eScience on Google at [email protected]
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Golden number - 1.618033989 Usually shortened to 1.618; doesn’t change number's value The Golden Ratio written as a proportion Background Image – The cross-section of a chambered nautilus shell, one of nature’s logarithmic spirals is sometimes debunked as a golden spiral, but a better or more approximate fit is the Golden Spiral on a 180 degree rotation. 1.618 - irrational number (can’t be expressed as a whole number or fraction) Ratio for beauty Never ends (in fi nite) or repeats What is the Golden Number
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Divide a line into two parts so that: The whole length divided by the longer length is also equal to the longer length divided by the shorter length. The Golden ratio Mathematical Proportion Diagram ÷ ÷ = 1.618… = What is a proportion? It is when two ratios or fractions are equal. A ratio compares values and shows how much of one thing is compared to another. Let’s look at the diagram below. , or phi
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2575 BC - Egyptian pyramid design has strong evidence for golden ratio 448-432 B.C. - Greek Parthenon design and proportions golden 490 - 430 B.C. - ancient Greek artist Phidias used golden ratio in sculpture work 428-347 B.C. - philosophers including Plato studied and used golden ratio in works Background Image – The pyramids of Giza, Egypt. 300 B.C. – mathematician, Euclid’s thirteen volume work Elements, referred to dividing line at point of 0.6180399; explained as way to divide a line in extreme and mean ratio 1200 A.D. - Fibonacci number series written about by Leonardo of Pisa aka Fibonacci & popularized in west History of the Golden Ratio & Fibonacci Numbers (2574 – 1200 AD)
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The Great Pyramid of Egypt has mathematical evidence for containing the golden ratio, Pi and the Pythagorean Theorem. Painting by G.W. Seitz 1878.
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448-432 B.C. Greek Parthenon - design and proportions found golden in column heights & widths & root support beam dividing line 428-347 B.C. Plato – described golden ratio in dialogue, Timaeus which describes 5 possible regular solids (Platonic solids: the tetrahedron, cube, octahedron, dodecahedron and icosahedron), some Platonic solids related to golden ratio The Parthenon Background image - Porch of Maidens or The Caryatid Porch of the Erechtheion, Athens, 421–407 BC.
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