#platonicsolid — Public Fediverse posts

Tried out some Lego sphere possibilities - here is one I quite like, could be classified as a cuboctahedron I suppose. Made from these triangular pieces joined by hinges in the corners.

The triangles are apparently known as "Plate, Modified 6 x 6 Hexagonal with Pin Hole" on Bricklink, the second hand Lego store. Pretty hard to find unless you order them from there

#Lego #geometry #platonicSolid

Tried out some Lego sphere possibilities - here is one I quite like, could be classified as a cuboctahedron I suppose. Made from these triangular pieces joined by hinges in the corners.

The triangles are apparently known as "Plate, Modified 6 x 6 Hexagonal with Pin Hole" on Bricklink, the second hand Lego store. Pretty hard to find unless you order them from there

#Lego #geometry #platonicSolid

Tried out some Lego sphere possibilities - here is one I quite like, could be classified as a cuboctahedron I suppose. Made from these triangular pieces joined by hinges in the corners.

The triangles are apparently known as "Plate, Modified 6 x 6 Hexagonal with Pin Hole" on Bricklink, the second hand Lego store. Pretty hard to find unless you order them from there

#Lego #geometry #platonicSolid

Tried out some Lego sphere possibilities - here is one I quite like, could be classified as a cuboctahedron I suppose. Made from these triangular pieces joined by hinges in the corners.

The triangles are apparently known as "Plate, Modified 6 x 6 Hexagonal with Pin Hole" on Bricklink, the second hand Lego store. Pretty hard to find unless you order them from there

#Lego #geometry #platonicSolid

Tried out some Lego sphere possibilities - here is one I quite like, could be classified as a cuboctahedron I suppose. Made from these triangular pieces joined by hinges in the corners.

The triangles are apparently known as "Plate, Modified 6 x 6 Hexagonal with Pin Hole" on Bricklink, the second hand Lego store. Pretty hard to find unless you order them from there

#Lego #geometry #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

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

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

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

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

Do you like making things out of paper?

I have an activity pack for you:
https://britthub.co.uk/shop/platonic-solids-paper-shapes-activity-pack/

I send you flat shapes, made from colourful card, plus instructions for folding and sticking. You fold and stick.

Joy is experienced at having made a thing. Maths and art, together as they should be.

#papercraft #mathstodon #math #platonicSolid #fediGiftShop #mastoArt #creativeToots #giftIdeas #artshop #artForSale #shopIndy #supportsmallBusiness #Christmas #ChristmasGifts

Do you like making things out of paper?

I have an activity pack for you:
https://britthub.co.uk/shop/platonic-solids-paper-shapes-activity-pack/

I send you flat shapes, made from colourful card, plus instructions for folding and sticking. You fold and stick.

Joy is experienced at having made a thing. Maths and art, together as they should be.

#papercraft #mathstodon #math #platonicSolid #fediGiftShop #mastoArt #creativeToots #giftIdeas #artshop #artForSale #shopIndy #supportsmallBusiness #Christmas #ChristmasGifts

Do you like making things out of paper?

I have an activity pack for you:
https://britthub.co.uk/shop/platonic-solids-paper-shapes-activity-pack/

I send you flat shapes, made from colourful card, plus instructions for folding and sticking. You fold and stick.

Joy is experienced at having made a thing. Maths and art, together as they should be.

#papercraft #mathstodon #math #platonicSolid #fediGiftShop #mastoArt #creativeToots #giftIdeas #artshop #artForSale #shopIndy #supportsmallBusiness #Christmas #ChristmasGifts

Apollonian gaskets based on Platonic solids. The vertices of a tetrahedron/octahedron/icosahedron are used for the centre positions of the initial circles. These are Riemann-sphere-mapped to the complex plane, where the gasket is iterated for more circles, and the result is mapped back onto the sphere. It's a little roundabout, but it works for me, and the heaviest part by far is drawing the visuals.

#apolloniancircles #apolloniangasket #riemannsphere #complexmath #platonicsolid #geometricart #fractal #fractalart #pythoncode #opengl #algorithmicart #algorist #mathart #laskutaide #ittaide #kuavataide #iterati

#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

@ftp_alun Just so! Feck the minor third. #PlatonicSolid

@ftp_alun Just so! Feck the minor third. #PlatonicSolid

@ftp_alun Just so! Feck the minor third. #PlatonicSolid

@ftp_alun Just so! Feck the minor third. #PlatonicSolid

@ftp_alun Just so! Feck the minor third. #PlatonicSolid

I was able to massively improve on yesterday's rendering of one #Kepler's representation of the #PlatonicSolid of Earth. Done in #Blender using hair curves for the grass.

I redid the grass with fewer control points (down from 8 to 3), then reduced the spline resolution from 12 to 3, and reduced the resolution of the profile curve from 12 to 2. Using some napkin math, each blade of grass was about 4608 verts before, and is now 72 now, so I could add 64 times as many blades as before.

A rendering of one #Kepler's representation of the #PlatonicSolid of Earth. Done in #Blender using hair curves for the grass.

Really feeling the limits of my hardware on this one. Blender crashed 4 times due to me running out of memory, and I had to make my grass way bigger than I wanted. There's probably a more optimal way I missed.

A transparent version will be posted in the replies when it's finished rendering.