#mathober2025 — Public Fediverse posts

Mathober in this weeks CodePen Spark! It was a really fun month of math doodles.

https://codepen.io/spark/480

@codepen

#mathober #mathober2025

Mathober in this weeks CodePen Spark! It was a really fun month of math doodles.

https://codepen.io/spark/480

@codepen

#mathober #mathober2025

Mathober in this weeks CodePen Spark! It was a really fun month of math doodles.

https://codepen.io/spark/480

@codepen

#mathober #mathober2025

Mathober in this weeks CodePen Spark! It was a really fun month of math doodles.

https://codepen.io/spark/480

@codepen

#mathober #mathober2025

Mathober in this weeks CodePen Spark! It was a really fun month of math doodles.

https://codepen.io/spark/480

@codepen

#mathober #mathober2025

#Mathober code is complete!

On codepen: https://codepen.io/collection/yyapOP

On OpenProcessing: https://openprocessing.org/curation/90042

#mathober2025

Thank you Everyone that participated - It was so inspiring to see all of the are, posts, humor and creations.

#Mathober code is complete!

On codepen: https://codepen.io/collection/yyapOP

On OpenProcessing: https://openprocessing.org/curation/90042

#mathober2025

Thank you Everyone that participated - It was so inspiring to see all of the are, posts, humor and creations.

#Mathober code is complete!

On codepen: https://codepen.io/collection/yyapOP

On OpenProcessing: https://openprocessing.org/curation/90042

#mathober2025

Thank you Everyone that participated - It was so inspiring to see all of the are, posts, humor and creations.

#Mathober code is complete!

On codepen: https://codepen.io/collection/yyapOP

On OpenProcessing: https://openprocessing.org/curation/90042

#mathober2025

Thank you Everyone that participated - It was so inspiring to see all of the are, posts, humor and creations.

#Mathober code is complete!

On codepen: https://codepen.io/collection/yyapOP

On OpenProcessing: https://openprocessing.org/curation/90042

#mathober2025

Thank you Everyone that participated - It was so inspiring to see all of the are, posts, humor and creations.

Today's #mathober is Minor.

I used minor arcs:

https://codepen.io/fractalkitty/pen/GgoXPjV

#mathober2025

Today's #mathober is Minor.

I used minor arcs:

https://codepen.io/fractalkitty/pen/GgoXPjV

#mathober2025

Today's #mathober is Minor.

I used minor arcs:

https://codepen.io/fractalkitty/pen/GgoXPjV

#mathober2025

Today's #mathober is Minor.

I used minor arcs:

https://codepen.io/fractalkitty/pen/GgoXPjV

#mathober2025

Today's #mathober is Minor.

I used minor arcs:

https://codepen.io/fractalkitty/pen/GgoXPjV

#mathober2025

Today's mathober:

https://codepen.io/fractalkitty/pen/vELazQL

#mathober2025

As a several-days-late contribution for the #Mathober Day 25 prompt ‘Wedge’, I would like to point out a little historical curiosity involving ‘wedge’.

Attached is a detail from an Old Babylonian clay tablet of geometrical problems and a reconstruction of the diagram.

The cuneiform text reads: ‘The square-side is 1 cable. ⟨Inside it⟩ I drew 12 wedges and 4 squares. What are their areas?’ (trans. Robson, ‘Mesopotamian mathematics’, p.95)

The term ‘wedge’ translates the Akkadian ‘santakkum’, which names any figure with three (possibly non-straight) sides. (1 ‘cable’ = approximately 360 metres)

The exact symmetry of the configuration is vital to the problem. Without symmetry, which is suggested by the (necessarily approximate) diagram, but which is not made explicit in the question, the ‘wedges’ could be (e.g.) non-isosceles triangles of different sizes, and the problem would be insoluble.

The problems on the tablet [https://www.britishmuseum.org/collection/object/W_1905-0515-1] comprise various geometric configurations in which symmetry is implicitly required for the solution.

#HistMath #HistSci #geometry #symmetry #Mathober2025

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https://codepen.io/fractalkitty/pen/ZYQjbqJ

Today's #mathober - a metabidiminished icosahedron

#mathober2025

Today's and yesterdays #mathober

Wedge:

https://codepen.io/fractalkitty/pen/azdKYOL

Amalgamation:

https://codepen.io/fractalkitty/pen/GgoGdgo

#mathober2025

Today's #mathober

https://codepen.io/fractalkitty/pen/Qwyroad

#mathober2025

Hope I did this right.

Here is the Jacobian for #mathober today:

https://codepen.io/fractalkitty/pen/bNEMBGO?editors=0110

Thanks @dpoulsen for the links and inspiration!

#mathober2025

I think I love Odious Numbers.

#mathober #mathober2025 #mathart #p5js

https://codepen.io/fractalkitty/pen/OPMvoOv

Today's #mathober is sawtooth:

https://codepen.io/fractalkitty/pen/MYKVYZw

#mathober2025

Today's #mathober

https://codepen.io/fractalkitty/pen/NPxyvZK?editors=0110

I was going to do more with the planes, but decided after a long run and a good day I needed to hug my banjo instead.

#mathober2025

Forgot to share yesterday's code for #mathober Domain:

https://codepen.io/fractalkitty/pen/PwZErMR?editors=0110

#mathober2025

Today's #mathober is primitive.

Here is a code snippet:

https://codepen.io/fractalkitty/pen/PwZEeEX?editors=0110

#mathober2025 #noKings

A very basic wheel for #mathober today
https://codepen.io/fractalkitty/pen/ByjJQYL

#mathober2025

Well - I tried something for today's #mathober "faithful"

https://codepen.io/fractalkitty/pen/ByjmGMq?editors=0110

#faithfulFunctor #mathober2025

#Mathober day 17: Wheel
#mathober2025
The concept of a #whizwheel are logarithmic scales on two circles which can be turned to calculate multiplications. It is the older form of a slide rule, but still used today in most flight schools and aviation exams despite the availability of electronic calculators.

The principle requires that you always know the order of magnitude for your answer. 10 means 0.1, 1, 10, 100, and so on.

#Mathober day 17: Wheel
#mathober2025
The concept of a #whizwheel are logarithmic scales on two circles which can be turned to calculate multiplications. It is the older form of a slide rule, but still used today in most flight schools and aviation exams despite the availability of electronic calculators.

The principle requires that you always know the order of magnitude for your answer. 10 means 0.1, 1, 10, 100, and so on.

#Mathober day 17: Wheel
#mathober2025
The concept of a #whizwheel are logarithmic scales on two circles which can be turned to calculate multiplications. It is the older form of a slide rule, but still used today in most flight schools and aviation exams despite the availability of electronic calculators.

The principle requires that you always know the order of magnitude for your answer. 10 means 0.1, 1, 10, 100, and so on.

#Mathober day 17: Wheel
#mathober2025
The concept of a #whizwheel are logarithmic scales on two circles which can be turned to calculate multiplications. It is the older form of a slide rule, but still used today in most flight schools and aviation exams despite the availability of electronic calculators.

The principle requires that you always know the order of magnitude for your answer. 10 means 0.1, 1, 10, 100, and so on.

#Mathober day 17: Wheel
#mathober2025
The concept of a #whizwheel are logarithmic scales on two circles which can be turned to calculate multiplications. It is the older form of a slide rule, but still used today in most flight schools and aviation exams despite the availability of electronic calculators.

The principle requires that you always know the order of magnitude for your answer. 10 means 0.1, 1, 10, 100, and so on.

Mathober Day 15: Chord

If you want to draw a convincingly round moon with craters, or a Jupiter with swirling vortices, then you need to draw circles in perspective on the surface of sphere. The key is doing this is drawing ellipses that are more circular in the center (eccentricity close to zero) and thinner near the edge (eccentricity close to one).

The precise way to do this requires a geometric construction shown on the right. Choose D, the height of the major axis for your ellipse. Draw a chord with height D on a circle, as far from the center horizontally as you want the ellipse to be. With D as the hypotenuse, draw a right triangle with legs horizontal (S) and vertical. Then D = S cos (alpha), where D is the major axis, S is the minor axis and alpha is the angle between D and S.

Comparison of the two paintings on the left shows how not using this principle (top) or using it (bottom) affect the illusion of that the painting is spherical. 
 #mathober #mathober2025 #mathart #watercolor

#Mathober #Mathober2025

The prompt for day 5 was 'Digraph Sink'. In mathematics 'digraph' is an abbreviation for 'directed graph' which is a kind of network made by joining nodes with arrows. A 'digraph sink' is any node which has no arrows that point out of it. If you walk around a digraph by following the arrows then the sinks are the places where you can get stuck.

In linguistics a 'digraph' is instead a pair of letters that make a different sound when written together than you would expect from their individual sounds. Let's draw a digraph digraph where the nodes are the letters of the alphabet, and the arrows represent which pairs of letters form digraphs.

The sinks in this digraph are B, D, F, H, J, K, L, M, V, X, Y and Z.

#Math #Maths #Mathematics #GraphTheory #Linguistics #Orthography #EnglishOrthography

#Mathober #Mathober2025

The prompt for day 4 was 'Strongly'. In linear algebra, the dual of a vector space V is the space V* of linear maps from V to the field. There's a natural inclusion 𝑉⊗𝑉* → Hom(𝑉,𝑉) and we call V *strongly* dualisable if and only if this map has an inverse.

The strongly dualisable vector spaces are precisely the finite dimensional ones. This is useful because it allows us to prove statements about finite dimensional vector spaces in a basis-free way. For example the trace is easy to define for strongly dualisable objects without mentioning any basis.

The same approach works for modules over a commutative ring. The strongly dualisable objects are precisely the finitely-generated projective modules. For example for ℤ this includes free modules like ℤ¹⁰ but not quotients like ℤ/12ℤ.

But if we work in higher algebra something interesting happens! In the category of chain complexes a chain is strongly dualisable if and only if it has finitely many nonzero modules, all of which are themselves strongly dualisable.

The ∞-category of chain complexes include the category of modules by sending V to … → 0 → 0 → 𝑉. But the chain complex … → 0 → 0 → ℤ/12ℤ is equivalent to … → 0 → ℤ → ℤ, which is dualisable!

So using ∞-categories we can extend the methods of finite-dimensional linear algebra to modules that were previously out of reach!

#Math #Maths #Mathematics #CategoryTheory #Homology #HomologyTheory

#Mathober #Mathober2025

The prompt for day 4 was 'Strongly'. In linear algebra, the dual of a vector space V is the space V* of linear maps from V to the field. There's a natural inclusion 𝑉⊗𝑉* → Hom(𝑉,𝑉) and we call V *strongly* dualisable if and only if this map has an inverse.

The strongly dualisable vector spaces are precisely the finite dimensional ones. This is useful because it allows us to prove statements about finite dimensional vector spaces in a basis-free way. For example the trace is easy to define for strongly dualisable objects without mentioning any basis.

The same approach works for modules over a commutative ring. The strongly dualisable objects are precisely the finitely-generated projective modules. For example for ℤ this includes free modules like ℤ¹⁰ but not quotients like ℤ/12ℤ.

But if we work in higher algebra something interesting happens! In the category of chain complexes a chain is strongly dualisable if and only if it has finitely many nonzero modules, all of which are themselves strongly dualisable.

The ∞-category of chain complexes include the category of modules by sending V to … → 0 → 0 → 𝑉. But the chain complex … → 0 → 0 → ℤ/12ℤ is equivalent to … → 0 → ℤ → ℤ, which is dualisable!

So using ∞-categories we can extend the methods of finite-dimensional linear algebra to modules that were previously out of reach!

#Math #Maths #Mathematics #CategoryTheory #Homology #HomologyTheory

#Mathober #Mathober2025

The prompt for day 4 was 'Strongly'. In linear algebra, the dual of a vector space V is the space V* of linear maps from V to the field. There's a natural inclusion 𝑉⊗𝑉* → Hom(𝑉,𝑉) and we call V *strongly* dualisable if and only if this map has an inverse.

The strongly dualisable vector spaces are precisely the finite dimensional ones. This is useful because it allows us to prove statements about finite dimensional vector spaces in a basis-free way. For example the trace is easy to define for strongly dualisable objects without mentioning any basis.

The same approach works for modules over a commutative ring. The strongly dualisable objects are precisely the finitely-generated projective modules. For example for ℤ this includes free modules like ℤ¹⁰ but not quotients like ℤ/12ℤ.

But if we work in higher algebra something interesting happens! In the category of chain complexes a chain is strongly dualisable if and only if it has finitely many nonzero modules, all of which are themselves strongly dualisable.

The ∞-category of chain complexes include the category of modules by sending V to … → 0 → 0 → 𝑉. But the chain complex … → 0 → 0 → ℤ/12ℤ is equivalent to … → 0 → ℤ → ℤ, which is dualisable!

So using ∞-categories we can extend the methods of finite-dimensional linear algebra to modules that were previously out of reach!

#Math #Maths #Mathematics #CategoryTheory #Homology #HomologyTheory

#Mathober #Mathober2025

The prompt for day 4 was 'Strongly'. In linear algebra, the dual of a vector space V is the space V* of linear maps from V to the field. There's a natural inclusion 𝑉⊗𝑉* → Hom(𝑉,𝑉) and we call V *strongly* dualisable if and only if this map has an inverse.

The strongly dualisable vector spaces are precisely the finite dimensional ones. This is useful because it allows us to prove statements about finite dimensional vector spaces in a basis-free way. For example the trace is easy to define for strongly dualisable objects without mentioning any basis.

The same approach works for modules over a commutative ring. The strongly dualisable objects are precisely the finitely-generated projective modules. For example for ℤ this includes free modules like ℤ¹⁰ but not quotients like ℤ/12ℤ.

But if we work in higher algebra something interesting happens! In the category of chain complexes a chain is strongly dualisable if and only if it has finitely many nonzero modules, all of which are themselves strongly dualisable.

The ∞-category of chain complexes include the category of modules by sending V to … → 0 → 0 → 𝑉. But the chain complex … → 0 → 0 → ℤ/12ℤ is equivalent to … → 0 → ℤ → ℤ, which is dualisable!

So using ∞-categories we can extend the methods of finite-dimensional linear algebra to modules that were previously out of reach!

#Math #Maths #Mathematics #CategoryTheory #Homology #HomologyTheory

#Mathober #Mathober2025

The prompt for day 4 was 'Strongly'. In linear algebra, the dual of a vector space V is the space V* of linear maps from V to the field. There's a natural inclusion 𝑉⊗𝑉* → Hom(𝑉,𝑉) and we call V *strongly* dualisable if and only if this map has an inverse.

The strongly dualisable vector spaces are precisely the finite dimensional ones. This is useful because it allows us to prove statements about finite dimensional vector spaces in a basis-free way. For example the trace is easy to define for strongly dualisable objects without mentioning any basis.

The same approach works for modules over a commutative ring. The strongly dualisable objects are precisely the finitely-generated projective modules. For example for ℤ this includes free modules like ℤ¹⁰ but not quotients like ℤ/12ℤ.

But if we work in higher algebra something interesting happens! In the category of chain complexes a chain is strongly dualisable if and only if it has finitely many nonzero modules, all of which are themselves strongly dualisable.

The ∞-category of chain complexes include the category of modules by sending V to … → 0 → 0 → 𝑉. But the chain complex … → 0 → 0 → ℤ/12ℤ is equivalent to … → 0 → ℤ → ℤ, which is dualisable!

So using ∞-categories we can extend the methods of finite-dimensional linear algebra to modules that were previously out of reach!

#Math #Maths #Mathematics #CategoryTheory #Homology #HomologyTheory

The #Mathober Day 9 prompt is ‘Chi’. In graph theory, \(\chi(G)\) denotes the chromatic number of a graph \(G\): the minimum number of colours required to colour all vertices so that no adjacent vertices have the same colour.

The famous ‘four colour theorem’ says that all planar graphs \(G\) have \(\chi(G) \leq 4\). A graph is planar if it can be drawn in the plane without any edges crossing.

The conjecture originated in 1852 when Francis Guthrie (1831–99) noticed that it was possible to colour a map of England using only four colours so that no neighbouring counties received the same colour, and wondered if this held true for all maps. The question for maps is transformed into one for graphs by replacing each region by a vertex and placing edges between vertices corresponding to neighbouring regions.

Thus, for the Mathober prompt ‘Chi’, I offer a map of the counties of England as they were in Guthrie's time and the corresponding graph, coloured in the same way with four colours.

Vector version (PDF format) of the map: https://ajcain.codeberg.page/posts/files/england-counties-map-4coloured.pdf

Vector version (PDF format) of the graph: https://ajcain.codeberg.page/posts/files/england-counties-graph-4coloured.pdf

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#Mathober2025 #GraphTheory #HistMath

A little Octagonal & Heptagonal walk

for #Mathober #Mathober2025 #Day8 #loop #geogebra

A little Octagonal & Heptagonal walk

for #Mathober #Mathober2025 #Day8 #loop #geogebra

A little Octagonal & Heptagonal walk

for #Mathober #Mathober2025 #Day8 #loop #geogebra

A little Octagonal & Heptagonal walk

for #Mathober #Mathober2025 #Day8 #loop #geogebra

A little Octagonal & Heptagonal walk

for #Mathober #Mathober2025 #Day8 #loop #geogebra

Today's Mathober - partial sum.

I also did a p5 sketch: https://codepen.io/fractalkitty/pen/ByjWppj?editors=0110

#mathober #mathober2025 #creativeCoding #birdart #mathart #mtbos #cantor #partialsums

Today's Mathober - partial sum.

I also did a p5 sketch: https://codepen.io/fractalkitty/pen/ByjWppj?editors=0110

#mathober #mathober2025 #creativeCoding #birdart #mathart #mtbos #cantor #partialsums

Today's Mathober - partial sum.

I also did a p5 sketch: https://codepen.io/fractalkitty/pen/ByjWppj?editors=0110

#mathober #mathober2025 #creativeCoding #birdart #mathart #mtbos #cantor #partialsums

Today's Mathober - partial sum.

I also did a p5 sketch: https://codepen.io/fractalkitty/pen/ByjWppj?editors=0110

#mathober #mathober2025 #creativeCoding #birdart #mathart #mtbos #cantor #partialsums