#goldenratio — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #goldenratio, aggregated by home.social.
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The #TCSAI #ConflagratoryResonanceAttractor is the 1st functional digital-physical isomorphic engine that generates persistent, measurable energy exclusively from the selective attraction of a single molecular unit C₁₃H₂₁N₄O₉P under #GoldenRatio. https://www.sonovamusicrecords.com/tcsai-conflagratory-resonance-attractor-phosphorescent-universe-neon #AI #ArtificialIntelligence
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The Bell Curve breathes like a cosmic lung while the Golden Spiral coils through Fibonacci's sacred ladder — probability and infinity dancing as one living equation written in the language of stars.
https://silverlenz.carrd.co
Zap ⚡ if it resonates — support the transmissions directly: https://silverlenz.github.io/zack-zaps/
#SacredGeometry #FibonacciSpiral #GoldenRatio #CosmicMathematics #ConsciousnessCode -
Endlich 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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The 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.
1/3
#GoldenRatio #GoldenSection #DivineProportion #HistMath #aesthetics #Zeising #Fechner
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The 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.
1/3
#GoldenRatio #GoldenSection #DivineProportion #HistMath #aesthetics #Zeising #Fechner
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The 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.
1/3
#GoldenRatio #GoldenSection #DivineProportion #HistMath #aesthetics #Zeising #Fechner
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The 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.
1/3
#GoldenRatio #GoldenSection #DivineProportion #HistMath #aesthetics #Zeising #Fechner
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The 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.
1/3
#GoldenRatio #GoldenSection #DivineProportion #HistMath #aesthetics #Zeising #Fechner
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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.
1/3
[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
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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.
1/3
[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
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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.
1/3
[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
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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.
1/3
[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
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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.
1/3
[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
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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.
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Stopping on 6 plays Gods music. The 7th cord plays the Devils tune. 7 imitates 1 in 6/6 time. Devil, once a deceptive angel. 369 harmonize. Wreck it with #FreeMason #penta and #hepta. We agree on #tri and #nona. #GoldenRatio is 123. Φ Pow6 equal pow5 plus pow7 where pow5 and pow7 equal.
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No 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
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Perfection.
#stormGoretti #mathematics #goldenratio #satellite #weather
original source:
x.com/WXWatcher07/status/2009394633022038045
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There’s a Problem With Photographers’ Obsession With The Golden Ratio https://petapixel.com/2025/12/28/theres-a-problem-with-photographers-obsession-with-the-golden-ratio/ #cartier-bresson #goldensection #Educational #composition #goldenratio #fibonacci #Vitruvius #davinci #davinci #art
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Today is Fibonacci Day. November 23 if written in MM/DD format recalls the #mathematician Leonardo Bonaccio of Pisa (c. 1170 - c. 1240 or 50) aka Fibonacci’s sequence (1,1,2,3…) where each number is the sum of the previous two. He used it to describe rabbit populations, but the sequence is commonly observed in nature, including in the spiral of a nautilus shell.🧵
#linocut #printmaking #mathematics #mathart #sciart #nautilus #GoldenRatio #GoldenSpiral #Fibonacci #fibonacciday2025 #FibonacciDay
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This piece was made in 2020. Inspired by exotic temples and sci-fi structures. As much as possible the proportions of the sculpture were designed within the golden ratio.
Shipped of to Zurich 5 years ago for still available pieces :thinkerguns:
#recycle #architecture #concrete #sculpture #brutalism #abstract #product #design #artifact #handmade #minimal #thailand
#unique #art #arquitectura #architektur #architettura #avantgarde #goldenratio #pi #zurich #zwitserland -
From Nautilus shells to the Parthenon, the Fibonacci sequence is nature's code for beautiful, balanced design.
This isn't just a mathematical curiosity; it's a practical tool for creating harmonious layouts and clear visual hierarchies in web design. Our new guide breaks down how to apply this timeless principle to your work.
Learn to design with nature's code: https://silphiumdesign.com/fibonacci-sequence-design-applying-natures-code/
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"Nature's Golden Ratio" by James DeFazio
Prints and much more available at: https://james-defazio.pixels.com/featured/natures-golden-ratio-james-defazio.html
#seashells #goldenratio #fineart #fineartphotography #doubleexposure #wallart #artwork #art #beachart #beachdecor #homedecor #interiordecor #mastoart #BuyIntoArt #ayearforart
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Gammel Estrup isn’t just a Renaissance manor—it encodes astronomy, alchemy, and sacred geometry. From golden spirals to Tycho Brahe’s stars, this Danish castle is an architectural cipher waiting to be read.
#GammelEstrup #AlchemyCastle #SecretGeometry #SacredMath #TychoBrahe #RenaissanceScience #ArchitectureMystery #GoldenRatio#ArchaeologyFinds #Storytelling #DidYouKnow #AncientHistory #HistoryFacts #DocumentaryShort #WeirdHistory -
Gammel Estrup isn’t just a Renaissance manor—it encodes astronomy, alchemy, and sacred geometry. From golden spirals to Tycho Brahe’s stars, this Danish castle is an architectural cipher waiting to be read.
#GammelEstrup #AlchemyCastle #SecretGeometry #SacredMath #TychoBrahe #RenaissanceScience #ArchitectureMystery #GoldenRatio#ArchaeologyFinds #Storytelling #DidYouKnow #AncientHistory #HistoryFacts #DocumentaryShort #WeirdHistory -
Gammel Estrup isn’t just a Renaissance manor—it encodes astronomy, alchemy, and sacred geometry. From golden spirals to Tycho Brahe’s stars, this Danish castle is an architectural cipher waiting to be read.
#GammelEstrup #AlchemyCastle #SecretGeometry #SacredMath #TychoBrahe #RenaissanceScience #ArchitectureMystery #GoldenRatio#ArchaeologyFinds #Storytelling #DidYouKnow #AncientHistory #HistoryFacts #DocumentaryShort #WeirdHistory -
Gammel Estrup isn’t just a Renaissance manor—it encodes astronomy, alchemy, and sacred geometry. From golden spirals to Tycho Brahe’s stars, this Danish castle is an architectural cipher waiting to be read.
#GammelEstrup #AlchemyCastle #SecretGeometry #SacredMath #TychoBrahe #RenaissanceScience #ArchitectureMystery #GoldenRatio#ArchaeologyFinds #Storytelling #DidYouKnow #AncientHistory #HistoryFacts #DocumentaryShort #WeirdHistory -
Golden Ratio Trick!
The Golden Ratio is ≈ 1.618. Use it for proportions! Example: if a=1, b=1.618.
#MathMagic #GoldenRatio -
Golden Ratio Trick!
The Golden Ratio is ≈ 1.618. Use it for proportions! Example: if a=1, b=1.618.
#MathMagic #GoldenRatio -
not too sure whether or not this meets the criteria but here's my shot for the fifth and last #thecompochallenge assignment: the golden spiral.
thanks @hiro for doing this!
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The Meter, Golden Ratio, Pyramids, and Cubits, Oh My — https://www.iforgeiron.com/topic/60514-the-meter-golden-ratio-pyramids-and-cubits-oh-my/
#HackerNews #Meter #GoldenRatio #Pyramids #Cubits #History -
@paysmaths
If you enjoyed that then you may also like this: https://www.youtube.com/watch?v=cCXRUHUgvLI
🙂
#Mathologer #GoldenRatio #maths
#mathematics #math -
Today is Fibonacci Day. November 23 if written in MM/DD format recalls the #mathematician Leonardo Bonaccio of Pisa (c. 1170 - c. 1240 or 50) aka Fibonacci’s sequence (1,1,2,3…) where each number is the sum of the previous two. He used it to describe rabbit populations, but the sequence is commonly observed in nature,
#linocut #printmaking #mathematics #mathart #sciart #GoldenRatio #GoldenRectangle #GoldenSpiral #Fibonacci #FibonacciSequence #fibonacciday2024 #FibonacciDay
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The many cousins of the Golden Ratio:
https://www.youtube.com/watch?v=cCXRUHUgvLI
#maths #GoldenRatio #mathematics #Mathologer #pentagon #heptagon #Ptolemy #Pythagoras -
Using Fibonacci Numbers to Convert from Miles to Kilometers and Vice Versa: https://catonmat.net/fibonacci-miles-kilometers
#fibonacci #fibonacciNumbers #GoldenRatio #Math #mathematics #units
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concrete Sculpture M1
2020 :pensive_party_blob:#goldenratio #scifiart #temple #exotic #monolith #sculpture #concrete #abstract #art #architecture #paperweight #geometric #model #contemporary #pyramid #brutalist
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Try to prove the following two results that relate the harmonic numbers to the golden ratio. Have an excellent weekend.
\[\displaystyle\sum_{n=1}^\infty\binom{2n}n\dfrac{H_n}{5^n}=2\sqrt5\ln\varphi\]
\[\displaystyle\sum_{n=1}^\infty\binom{2n}n\dfrac{H_n}{5^nn}=\frac{2\pi^2}{15}-2\ln^2\varphi\]
where \(\varphi=\frac{1+\sqrt5}2\) is the golden ratio; and \(H_n=\left(1+\frac12+\frac13+\ldots+\frac1n\right)\) is the \(n\)-th harmonic number.
#GoldenRatio #HarmonicNumbers #HarmonicNumber #Logarithm #Pi #Summation #Math #Sum #InfiniteSum #Binomial #BinomialCoefficient #Maths #WeekendChallenge
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My nautilus with golden rectangle print for Fibonacci Day. November 23 if written in MM/DD format recalls the #mathematician Leonardo Bonaccio of Pisa (c. 1170 - c. 1240 or 50) aka Fibonacci’s sequence (1,1,2,3…) where each number is the sum of the previous two. He used it to describe rabbit populations, but the sequence is commonly observed in nature, 🧵1/2
#linocut #printmaking #mathematics #mathart #sciart #nautilus #GoldenRatio #Fibonacci #fibonacciday2023 #FibonacciDay #MastoArt
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The prompt for day 10 is 'Nowhere-Neat'. In mathematics, a nonwhere-neat tiling is one where no two tiles share an edge (they do meet at their edges, but one edge is always a different size or offset, so they don't share the entire edge).
As it turns out, the tiling I made for day 9 was already nowhere-neat (https://mathstodon.xyz/@OscarCunningham/111229992806552483). But yesterday I screwed up the colouring in the image. I tried to use three colours so no adjacent tiles have the same colour. But in fact this is impossible. You can see at the bottom of the image two white rectangles are next to each other.
So I corrected the colouring to use four colours, worked out how to colour the parts with negative x coordinate, and mapped the whole thing to the disc model of the hyperbolic plane.
#Math #Maths #Mathematics #Hyperbolic #HyperbolicGeometry #HyperbolicTilings #Fibonacci #GoldenRatio
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The prompt for day 9 is 'Hierarchy'. This reminded me of the binary tiling (https://en.wikipedia.org/wiki/Binary_tiling), where every square is arranged in a hierachy with a manager and two subordinates.
So I decided to figure out how to do the same thing with base ϕ (https://en.wikipedia.org/wiki/Golden_ratio_base) in place of binary.
#Math #Maths #Mathematics #Hyperbolic #HyperbolicGeometry #HyperbolicTilings #Fibonacci #GoldenRatio
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New paper: "W. D. Hamilton and the golden sex ratio" (#OpenAccess)
https://doi.org/10.1016/j.jtbi.2023.111599
#GoldenRatio #SexRatio #SexAllocation #Haplodiploidy #MaleHaploidy#Image https://hotpot.ai/art-generator #OA
