#mathober — Public Fediverse posts

For Genuary 9, a crazy automaton, I'm combining a cellular automaton with the concept of "odious numbers" I learned about during #mathober. Each cell is assigned one of 4 states, and if sum of states of 8 surrounding cells is an odious number, increment the state. Otherwise go back to 0.

#genuary #genuary9 #genuary2026 #odious #automaton

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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I haven't been posting for #mathober, but have been messing with compass and straightedge constructions, colored in with something like watercolor or pencil. Today's prompt, "chord", seems to fit this construction of a pentagon, which involves placing 5 chords within a circle.

#mathtober #euclid #geometry #chord #mathart #pentagon

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

The #Mathober day 3 prompt is ‘#Polyhedron’. I have no art to offer, but I thought I would use the occasion to draw attention to a lesser-known role of polyhedra in Johannes Kepler's (1571–1630) thought.

Start with the famous part: Kepler argued that the five regular (or Platonic) solids fitted between the orbs of the then-known six planets [https://commons.wikimedia.org/wiki/File:Kepler-solar-system-1.png].

When Galileo discovered four moons of Jupiter, Kepler sought a similar polyhedral structure for the Jovian system, and suggested that ‘semiregular’ solids provided the key. ‘Semiregular’ for Kepler meant that the polyhedra had rhombic faces and satisfied certain technical criteria. (The concept differs from today's notion of semiregular polyhedra.)

There were exactly three such ‘semiregular’ polyhedra:

• the cube (the square being a special kind of rhombus).

• the rhombic dodecahedron (12 faces; diagram attached).

• the rhombic triacontahedron (30 faces; diagram attached).

Kepler placed the rhombic dodecahedron between Io and Europa, the rhombic triacontahedron between Europa and Ganymede, and the cube between Ganymede and Callisto.

Kepler thought that there were six planets because God had shaped the cosmos around the five platonic solids. The three ‘semiregular’ solids would similarly explain why there were four moons of Jupiter.

Perhaps someone who is a better artist than I am could draw a diagram of the three rhombic solids and the orbs of the four Galilean moons in the style of Kepler's famous diagram of the Platonic solids between the orbs of the planets.

#Mathober2025 #HistMath #HistSci

polynomial:

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

#wiggle #mathober #mathober2024 #polynomial

Triangle-shaped model to idolise clothes (7) #mathober #cryptic #yesterdays #istheschedulerevenworking

It might be natural wood (3) #mathober #cryptic #yesterdays #scheduledtootthatdidntsend #grrr

And we're halfway through the month! Folks doing creative challenges, how's it going? Have you been able to keep up? What are some of your favorite submissions so far?

And what are you all looking forward to next month?

#challenge #CreativeChallenge #crawltober #hacktober #hacktoberfest #inktober #LOLtober #looptober #mathober #RetroChallenge #WeirdWebOctober

Dip containing chickpeas (but no uranium) bearing manufacturer's symbol in corresponding proportion (10) #mathober #cryptic #yesterdays #oops

Day1 - Kiss!

I am going to try to combine procreate and p5js for this year.

Full page: https://codepen.io/fractalkitty/live/yLGELmY

Code on CodePen: https://codepen.io/fractalkitty/pen/yLGELmY

OpenProcessing: https://openprocessing.org/sketch/2027277

I will post as I do stuff here:
#Mathober2023 #Mathober #mathart #gasket #circlePacking #kiss