bewitchedmindEndlich mal wieder ein langes Video von Tibees. Including: eine lange überfällige Übersetzung eines Weltklassikers, Erklärung des Worts "buttload" und ein Rant über Mathe-Esoterik.
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Alan J. CainThe idea that the ‘golden’ ratio — $1.61803\ldots:1$ — has applications in visual art and architecture does not go back any further than the 2nd edition (1799–1802) of Jean-Étienne Montucla's (1725–99) (generally superb) ‘Histoire des Mathématiques’, in which he made the **incorrect** statement that Luca Pacioli's (c.1447–1517) book ‘Divina Proportione’ included illustrations of the ratio's application to architecture and font design.
This was shortly after the earliest known appearance of the term ‘golden section’ in Johann Samuel Traugott Gehler’s (1751–95) general scientific dictionary ‘Physikalisches Wörterbuch’.
The golden ratio was then taken up by Adolph Zeising (1810–76) as the basis for a system of aesthetic proportion in his book ‘New Theory of the Proportions of the Human Body’ (1854), where he argued — apparently to his own satisfaction — that his system agreed with the proportions of many masterpieces of art.
The psychologist Gustav Fechner (1801–87) made a much-misreported experiment in which people were asked to choose the most aesthetically pleasing of various rectangles (shown in the attached image). The most popular choice was the 34 ∶ 21 rectangle, whose proportions approximate the golden ratio. Fechner's conclusion was only that **a range of rectangles**, including the golden ratio rectangle, were considered most pleasing.
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#GoldenRatio #GoldenSection #DivineProportion #HistMath #aesthetics #Zeising #Fechner
Luca Pacioli’s (c.1445–1517) book ‘Divina proportione’ (written 1496–8, published 1509) is famous in the history of mathematical beauty, but mostly for the wrong reasons.
The term ‘divine proportion’ refers to Euclid's ‘extreme and mean ratio’, known since the late 18th century as the ‘golden ratio’: $1.61803\ldots:1$.
Pacioli's use of the term ‘divine’ **was not based upon aesthetic appreciation**.
Rather, he made a mystical identification of certain properties of the ratio with attributes of God. E.g., the incommensurability of the ratio = the indefinability and ineffability of God.
But Pacioli aesthetically admired the five regular polyhedra — the platonic solids — and the archimedean solids that he knew. In the dedication of ‘Divina proportione’ he wrote that hoped that his patron would see ‘their most sweet harmony’. He linked the aesthetic value of the solids to that of the sphere, from which he saw them as deriving. He seems to have placed special value on the ‘most noble’ dodecahedron.
In his portrait (attached), a dodecahedron sits on top of one of his books as a symbol of mathematical success. His diagram is part of the construction of the tetrahedron. A glass rhombicuboctahedron hangs behind him.
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[Each day of February, I am posting a short interesting story/image/fact/anecdote related to the aesthetics of mathematics.]
#GoldenRatio #DivineProportion #MathematicalBeauty #MathArt #polyhedron #RegularSolid #PlatonicSolid
earthlingTake something as simple as a line segment and mark it at just the right place. Looking at it with a mathematician's eye, an interesting relationship appears: the ratio between the whole line and the larger of the pieces it was broken into is the same as the ratio of the larger piece and smaller piece. Better known as "the golden ratio" or phi, 1.618- is a number that has fascinated humans for several hundred years, and people have claimed evidence of phi in all manner of things.
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#GoldenRatio
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#GoldenRatio
See also:
The Golden Ratio by Mario Livio, 2003
The Story of Phi, the World's Most Astonishing Number
Most readers will have at least dim memories from geometry class of the irrational number pi. Theoretical astrophysicist Livio gives pi's overlooked cousin phi its due with this lively account, the first on the subject written for the layperson.
The Golden Ratio by Gary B. Meisner, 2018
The Divine Beauty of Mathematics
The Golden Ratio examines the presence of this divine number in art and architecture throughout history, as well as its ubiquity among plants, animals, and even the cosmos. This gorgeous book features clear, entertaining, and enlightening commentary alongside stunning full-color illustrations by Venezuelan artist and architect Rafael Araujo.
Christian
NicholasNo riddle this time, or perhaps a very big one. Did you know that the Great Pyramid is roughly proportional to the sides of Kepler's triangle? The what? Yes, you heard that right.
#maths #geometry #goldenratio #kepler #pseudoscience #hiddenarcheology
Joris MeysPerfection.
#stormGoretti #mathematics #goldenratio #satellite #weather
original source:
x.com/WXWatcher07/status/2009394633022038045
w4v3#03 Fibonacci Forever.
Chaos or not? For art, architecture and in nature. The Fibonacci numbers always look "nice". And where do you find them here?
Again minimalism with circles having the radius from 1 starting, then 2, 3, 5, 8, ... until the image width is reached. Simple yet satisfying.
It's again inspiring to see all your interpreations of each prompt. Thanks.
#genuary #genart #circle #fibonacci #goldenratio #art #mastoart #fediart #p5js #noai #genuary2026 #code #math #programming #artwork #minimalism #coding #generativeart #generative #artforsale #simplify #creativecoding #chaos
