5/3/2023 0 Comments Oe goldenratio![]() “I never saw that before,” says the impressed Hasid. He doodles some more Fibonaccis across the stock market pages of the newspaper. Now Max is interested, because those are Fibonacci numbers. The Hebrew word for “east” adds up to 144, the Hasid explains, and “the Tree of Life” comes to 233. He meets a Hasidic man who gets him interested in Jewish numerology, the practice called gematria where a word is turned into a number by adding up the numerical value of the Hebrew letters it contains. The main character of the movie is a number theorist named Max Cohen who thinks extremely intensely and twirls his fingers in his hair a lot. The friend of a friend was named Darren Aronofsky, and his movie Pi came out in 1998. We ate patty melts, I told him some stories, I forgot about it, years went by. He said he was making a movie about math and wanted to talk to a practitioner about what the mathematical life was really like. One day in the ’90s, I had dinner with a friend of a friend at the Galaxy Diner in New York. There’s a small but persistent school of financial analysis which holds that the golden ratio governs fluctuations in the stock market your Bloomberg terminal, should you be flush enough to have one, will draw little “Fibonacci lines” on the stock charts for you. An influential 1978 paper in the Journal of Prosthetic Dentistry suggests that a set of false teeth, for maximum smile appeal, should have the central incisor 1.618 times the width of the lateral incisor, which should in turn be 1.618 times as wide as the canine. The number theorist George Ballard Mathews was already complaining about it in 1904, writing that “the ‘divine proportion’ or ‘golden section’ impressed the ignorant, nay even learned men like Kepler, with a sense of mystery, and set them a dreaming all kinds of fantastic symbolism.” Figures with lengths in golden proportion to one another are sometimes said to be inherently the most beautiful, though the claims that the Great Pyramid of Giza, the Parthenon, and the Mona Lisa were all designed on this principle aren’t well substantiated. Hofstetter, Another 5-step Division of a Segment in the Golden Section, Forum Geometricorum, v 4 (2004), pp.There’s been a miasma of mysticism around the golden ratio for a long time. $IG/GH = DI/FH = (\sqrt=\varphi.$ References ![]() To see why this is so, let $I$ be the intersection of $CD$ and $AB$ and $H$ the foot of perpendicular from $F$ to $AB.$ For a given segment $AB$ of length $1,$ form circles $A(B)$ and $B(A).$ Let $C$ and $D$ be the intersections of $A(B)$ and $B(A).$ Extend $AB$ beyond $A$ to the intersection $E$ with $A(B).$ Draw $E(B)$ and let $F$ be the intersection of $E(B)$ and $B(A)$ farther from $D.$ $DF$ intersects $AB$ in $G.$ $AG:BG = \varphi. More recently (30 May, 2016), Tran Quang Hung found in the same diagram additional instances of the famous number. In the resulting diagram, Hofstetter observes not one but two occurrences of the Golden Ratio. Hofstetter presented several 5-step construction of the Golden Ratio. In the early 2000s, in a series of papers, K. 5-Step Construction of the Golden Ratio, One of Many
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