#mathober day 14: Icositetragon

A 24-sided regular polygon, divided into 66 rhombs! Pop art style!

#mathober2026 #math #geometry

#mathober day 13: Standard Map

Imagine a 2D pendulum in zero gravity. Pick an initial angle and momentum. Then, at regular intervals, "kick" the end of the pendulum forward with strength sin(angle). This is a very simple system that exhibits chaotic behavior!

If you place a dot on a diagram after each kick according to the current angle (x-axis) and momentum (y-axis), you get the "standard map". Here is an artist's impression for kick-strength 0.971635!

#mathober2026 #math #chaostheory

I'm in #Mainz and #Wiesbaden for a week! Do I know people here who would show me the local hackspaces or other nerdy places? Also happy about any recommendations for good vegan food, or whatever else to see or do! :)

Obligatorisch: Das wichtige an funktionierende Software ist nicht der Code, sondern Organisation, Absicht und Vertrauen dahinter.

Und das fehlt bei den gesloppten Projekten halt in den allermeisten Fällen. Die werden gebaut für 5 Minutes of Fame. Dann ist der Dopamin Kick weg, und es würde nur extrem viel Arbeit warten

#mathober day 12: Reciprocal Prime Constant

Add up the reciprocals of all primes up to n. How far is this away from ln(ln(n)), as n gets large?

The plot of these two functions reminded me of a bridge. Can you find the constant being visualized here?

#mathober2026 #math #numbertheory

#mathober day 11: Problem of Points

Two players toss coins, and whoever wins 5 rounds first wins the entire pot. But: Someone interrupts the game as one player has won 3 rounds, and the other one 1. How should they split the pot now?

This problem motivated our modern probability theory and the concept of the "expected value".

Here's a "tree" diagram depicting the situation I described. Can you read from it how the players should split the pot?

#mathober2026 #math #probabilitytheory

#mathober day 10: Simple Pole

I learned a lot about complex analysis today! Here's one way to visualize the function f(z) = 1/z, where z is a complex number. The height represents the real part of the result, while the hue represents the "angle" of the complex number.

This particular function has a "pole" at the origin, where it blows up to infinity. It's "simple" (has order 1), because it's "only" a 1/z blow-up. I think a 1/z^2 blow-up would have order 2?

#mathober2026 #math #complexanalysis

In light of the recent news about the 3 dimensional aperiodic monotile (https://arxiv.org/pdf/2609.24779v1) Here an animation of the assembly of the rep-tile it is based on

"Post no signs" 🙃

#mathober day 9: K-Cyclic Graph

These are the twelve 7-cyclic graphs! Start on any node, and then follow 7 edges (you can re-use edges), visiting all nodes, and start back at the beginning. These are all graphs that allow that.

#mathober2026 #math #graphtheory

#mathober day 8: Parabolic Rotation

I rotated some parabolas around their vertex, and the result reminded me of dahlias!

#mathober2026 #math

#mathober day 7: Five Circles Theorem

Arrange five circles so that their intersections are distributed around a sixth circle. Draw a pentagram through their second intersections. Then its tips will always also lie on the circles!

First time experimenting with #krita's watercolor brushes, happy with how that turned out. 🎨🖌️

#mathober2026 #math #geometry

#mathober day 6: Connected Topology

Learned about the "Topologist's Sine Curve", sin(1/x), defined on (0,1], together with the origin. The question: Is it "connected"?

Turns out that it's neither path-connected (the duck can't reach the horizon) nor locally connected (no matter how small you make the "sun disk", the river that overlaps it will never be one piece) , but still "connected" (there's no gap between river + sun you could cut along). Weird!

#mathober2026 #math #topology

#mathober day 5: Inellipse

Any convex pentagon has a uniquely determined ellipse that touches all of its sides from the inside!

For a quadrilateral, is seems that there's basically one "degree of freedom" – you can squish and stretch it!

For a triangle, there's two degrees of freedom: Rotation and squishyness (aka eccentricity).

One way to construct a pentagon's inellipse involves a pentagram, so here's a witchy diagram for the three types of shapes.

#mathober2026 #math #geometry

#mathober day 4: Linear Recurrence

I played around with the sequence x_n = x_{n-1} + x_{n-2} + x_{n-3}, which I later learned is called the "Tribonacci sequence"! :D

I tried a couple of ways to visualize it – here's my favorite one! Note how the side length of one square always equals the sum of the three terms in the sequence before it! You then have to copy each square once to another location to derive the size of the square three steps after it.

#mathober2026 #math

#mathober day 3: Permutation List

Made in #krita, using memileo's fantastic impasto brush set! https://www.opendesktop.org/p/2161272/ (Thanks to @mkasu for the recommendation!)

#mathober2026 #math #combinatorics #grouptheory

#mathober day 2: Zebra Graph

The zebra is an unorthodox chess piece that's a bit like the knight, but it jumps 3 by 2 squares instead of 2 by 1! A zebra graph describes all of its possible moves on a grid.

I spotted one in the wild!

#mathober2026 #math

#mathober
1: Perimeter of an Ellipse

Me: "Okay, so if I squish my circle into an ellipse, can I still calculate the area?"
Maths: "yeah no problem, it's basically the same thing as with a circle, substitute πr² with πab easy-peasy!"
Me: "oh cool, so the circumference of the circle will be similar to 2πr, right?"
Maths:

Today is the first day of #mathober (a month of mathematical creativity prompts, see https://mathober.com for details) and I've done a thing: it's a zine about today's prompt, the boundary of an ellipse! PDF here: https://katiesteckles.co.uk/mo1

Happy #mathober to those who celebrate!

Day1: Perimeter of an Ellipse
Day 5: Inellipse

#generativeArt #mathart #loop #animation #processing #mathober26,