#platonicsolid — Public Fediverse posts

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

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

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

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

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

I find it fascinating how #ChristmasTrees have become much more #abstract in #London this year.
Fewer trees (fake or real) Instead, an array of semi-plantonic cones, shining with light. More likely made of #baubles than having them hanging.
What will #Christmas evolve into next?

#photography #ThickTrunkTuesday #PlatonicSolid

I find it fascinating how #ChristmasTrees have become much more #abstract in #London this year.
Fewer trees (fake or real) Instead, an array of semi-plantonic cones, shining with light. More likely made of #baubles than having them hanging.
What will #Christmas evolve into next?

#photography #ThickTrunkTuesday #PlatonicSolid

One of my earliest #CSS #3D demos on @codepen: how to (de)construct a dodecahedron https://codepen.io/thebabydino/pen/ALQVQe

A dodecahedron is one of the 5 regular polyhedra = made up of only identical regular polygon faces. Regular polygons have all edge lengths and vertex angles equal.

#geometry #Maths #code #coding #css3D #cssTransforms #transform #frontend #polyhedron #polyhedra #PlatonicSolid #dodecahedron #cssAnimation #web #dev #webDev #webDevelopment #trigonometry #Sass #SCSS

One of my earliest #CSS #3D demos on @codepen: how to (de)construct a dodecahedron https://codepen.io/thebabydino/pen/ALQVQe

A dodecahedron is one of the 5 regular polyhedra = made up of only identical regular polygon faces. Regular polygons have all edge lengths and vertex angles equal.

#geometry #Maths #code #coding #css3D #cssTransforms #transform #frontend #polyhedron #polyhedra #PlatonicSolid #dodecahedron #cssAnimation #web #dev #webDev #webDevelopment #trigonometry #Sass #SCSS

One of my earliest #CSS #3D demos on @codepen: how to (de)construct a dodecahedron https://codepen.io/thebabydino/pen/ALQVQe

A dodecahedron is one of the 5 regular polyhedra = made up of only identical regular polygon faces. Regular polygons have all edge lengths and vertex angles equal.

#geometry #Maths #code #coding #css3D #cssTransforms #transform #frontend #polyhedron #polyhedra #PlatonicSolid #dodecahedron #cssAnimation #web #dev #webDev #webDevelopment #trigonometry #Sass #SCSS

One of my earliest #CSS #3D demos on @codepen: how to (de)construct a dodecahedron https://codepen.io/thebabydino/pen/ALQVQe

A dodecahedron is one of the 5 regular polyhedra = made up of only identical regular polygon faces. Regular polygons have all edge lengths and vertex angles equal.

#geometry #Maths #code #coding #css3D #cssTransforms #transform #frontend #polyhedron #polyhedra #PlatonicSolid #dodecahedron #cssAnimation #web #dev #webDev #webDevelopment #trigonometry #Sass #SCSS

#MaxTegmark - What Exists?

https://www.youtube.com/watch?v=FIsD70ZLUbo

#Philosophy #PhilosophyOfScience #Science #Metaphysics #Physics #LawsOfNature #LawsOfPhysics #Existence #Multiverse #Math #Maths #Mathematics #Observer #Observers #Ideas #Numbers #AbstractObjects #Platonism #PlatonicSolids #PlatonicSolid #CloserToTruth #RobertKuhn

#MaxTegmark - What Exists?

https://www.youtube.com/watch?v=FIsD70ZLUbo

#Philosophy #PhilosophyOfScience #Science #Metaphysics #Physics #LawsOfNature #LawsOfPhysics #Existence #Multiverse #Math #Maths #Mathematics #Observer #Observers #Ideas #Numbers #AbstractObjects #Platonism #PlatonicSolids #PlatonicSolid #CloserToTruth #RobertKuhn

#MaxTegmark - What Exists?

https://www.youtube.com/watch?v=FIsD70ZLUbo

#Philosophy #PhilosophyOfScience #Science #Metaphysics #Physics #LawsOfNature #LawsOfPhysics #Existence #Multiverse #Math #Maths #Mathematics #Observer #Observers #Ideas #Numbers #AbstractObjects #Platonism #PlatonicSolids #PlatonicSolid #CloserToTruth #RobertKuhn

#MaxTegmark - What Exists?

https://www.youtube.com/watch?v=FIsD70ZLUbo

#Philosophy #PhilosophyOfScience #Science #Metaphysics #Physics #LawsOfNature #LawsOfPhysics #Existence #Multiverse #Math #Maths #Mathematics #Observer #Observers #Ideas #Numbers #AbstractObjects #Platonism #PlatonicSolids #PlatonicSolid #CloserToTruth #RobertKuhn

#MaxTegmark - What Exists?

https://www.youtube.com/watch?v=FIsD70ZLUbo

#Philosophy #PhilosophyOfScience #Science #Metaphysics #Physics #LawsOfNature #LawsOfPhysics #Existence #Multiverse #Math #Maths #Mathematics #Observer #Observers #Ideas #Numbers #AbstractObjects #Platonism #PlatonicSolids #PlatonicSolid #CloserToTruth #RobertKuhn