#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?
#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!
#mathober day 14: Icositetragon
A 24-sided regular polygon, divided into 66 rhombs! Pop art style!
#mathober day 15: Irredundant
Here's a game for you: Select some nodes from this graph, so that:
1. All nodes of the graph are either in your set or neighbors of your set (your set is "dominating"), and
2. You can't remove nodes from your set without losing that property (your set is "irredundant").
How small can you make your set? How big? Can you tell why?
#mathober day 16: Isochronous Curve
There was a YouTuber called Murph
who let marbles race, and observe:
All of them, how sublime,
arrived at the same time
for the track was an isochrone curve.
#mathober day 17: Dimension Invariance
A coffee cup is a donut
but certainly not
a napkin
even one with a hole.
No matter how hard you
squish and stretch
R^2 and R^3 can't ever be
homeomorphic.
#mathober day 18: Biflecnodal Point
Still traveling, and deprioritizing making big drawings! So here's a haiku! :)
One inflection point
on top of a second one
that's a biflecnode!
#mathober day 19: Orthic Triangle
find all heights of a triangle, connect their feet: orthic triangle
wear one as a child to straighten your teeth: orthodontic triangle
tool to help you find typos on a page of text: orthographic triangle
common bird classification system: ornithological triangle
seat profile that prevents hurting spines: orthopedic triangle
important doctrines after the great geometric schism: orthodox triangle
keyboard nerds love to type on these: ortholinear triangle
#mathober day 20: Nice Vector Field
What researching today's prompt feels like:
#mathober day 21: Prime Ring
One ring to contain them all,
one ring to identify them,
one ring to imply them all,
and in the domain bind them.
@blinry hmmm. The sum term as well as the log terms both diverge. I think we can use the prime density function somehow, as primes are distributed logarithmically as well…?
(coffee is broken, no brain left for the rest)
The setting in an Italian Renaissance city is (imo) well-chosen for mathart. And there's a hyper-para-superbolic rotational body in the background that goes well with the other day's prompt.
@blinry I can't unsee this! love it
@blinry This makes me want to read the comic book
Oct 15, 2026, 5:41 PM@blinry This combination of properties seems to be what is usually just called "minimal dominating", the smallest ones are "minimum dominating".
Can you find a graph with a maximal irredundant set that is not dominating?
@tian I don't think so! Proof attempt: If S is irredundant, but not dominating, there is a node that's neither in S nor neighboring S. So we can add that node to S without making S redundant. So S was not maximal irredundant.
Oct 16, 2026, 10:19 AM@blinry Certainly the new node is needed for domination, but are all nodes in S needed?
@blinry I choose {5, 7, 14}. That should satisfy it, and I don't think 2 nodes are possible. Since 8 is only connected to 7 either 8 or 7 needs to be in the set. Taking 8 instead of 7 "feels" wrong, 7 "gains more ground".
@envy Neat, yeah, I think 3 ist the "minimum" size. Not quite sure about the largest set yet!
@blinry I can get up to 5 I think: {1, 6, 8, 12, 14}
@LaurinMurer @envy Seems irredundant to me! Neat!
@blinry I love this
@blinry The first part seems simple enough, since a minimal dominating set is irredundant. To cover 8, we must pick either 7 or 8, and 7 is a better choice. Of the remaining uncovered graph, no one is sufficient, but 5 and 14 are. So, it can be made as small as three, and no smaller.
@blinry nice!
Oct 17, 2026, 12:54 PM@blinry
Dimension is the exact thing that homotopy forgets about
@blinry but only if it has one handle, right?
@blinry when two inflections touch, it is called as such: that's biflecnode! 🎶
@blinry love the poetry :)
@blinry i love love love your posts
@blinry shape of Isengart: Orthanc triangle
@blinry I feel like I need to doodle ornithological triangle
- this made my day
@fractalkitty Also thought of you when writing that, of course! ;)
Can't agree more.
@blinry ha, love it!
@blinry precioussssss
Oct 21, 2026, 9:07 PM@blinry
Beautiful :)
@blinry 100%
@fractalkitty @blinry
And yet ... all fun little arrows.
linear algebra = just vectors
abstract algebra = just think vectors 😊