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@witch--of--agnesi
Explaining a beautiful mathematical concept and the person asks for the real world application like bitch first off the real world application is it makes me personally ecstatic and second it doesn't need one because it's my special little princess concept
i dont think thats what laymen means
Hey so you remember this thing that everyone on mathblr got excited about recently?
This is the hat, and it's what's called an "aperiodic monotile". This means that no matter how you arrange copies of this tile, you can never get an arrangement that will repeat infinitely (think of it like the irrational numbers of tilings). This was big news in mathematics as while sets of more than one tiles have been found that are aperiodic (e.g: The Penrose Tiles), this was the first tile that's aperiodic by itself, hence "monotile". (There are some caveats to this but that's not important for understanding this post)
However.
If you look at images of the hat tiling, you may notice something.
If you look at the tiles labled 1 and 2, you'll see that one's a reflected copy of the other. In fact, any infinite arrangement with hats requires you to you mix unreflected and reflected tiles. Which raises the question: is it possible to have an aperiodic monotile that doesn't need reflections?
Presenting the Spectre, A chiral aperiodic monotile.
Using only translation and rotation, any arrangement of copies of this tile will never repeat.
Mathematically speaking, this is really fucking cool.
The paper on it is still in preprint, but hopefully I won't need to retract this post. A copy of it can be found here and a post going into some more details of how the shape was discovered is here.
I want weird math textbooks. Group theory textbooks in the style of a comic book. Real analysis textbooks written as a long dialogue between forest animals. Elaborate romantic fan fictions about the relationships between Lie groups and their corresponding Lie algebras.
Have you read Surreal Numbers: How Two Ex-Students Turned On to Pure Mathematics and Found Total Happiness? It's an introduction to the concept of surreal numbers told through a conversation between two people coming up with the theory together while hanging out at the beach. I borrowed it from my uni library purely for fun (it had nothing to do with any of my actual modules) and it made an interesting change from straight-forward textbooks.
repeat after me:
on the other side of fear, there is relief. on the other side of fear, there is success. on the other side of fear, there is love. on the other side of fear, there is joy. on the other side of fear, there is contentment. on the other side of fear, there is result. i decide that my fear is not an ocean; it is a line.
The Closing Ceremonies for Math Poetry Month 2021
I have a lot more to say about math and poetry, and I will save most of it for next April, I think. All I can say for now is that math and poetry continue to be powerful forces in my life, and I hope at least a few people gained something from this little project of mine. What I want to end this first Math Poetry Month on is some suggested reading:
1. Strange Attractors: Poems of Love And Mathematics edited by Sarah Glaz and JoAnne Growney
This poetry anthology is full of amazing math poems by the likes of Emily Dickinson, Shel Silverstein, Bernoulli, and Lewis Carroll, and it is all the proof you need that math and poetry have a deep connection. If you are just starting out with math poetry, I think this is the essential body of work. These two women are also active in the world of math poetry, so going to either of their websites is a treat!
2. A Mathematician’s Apology by G.H. Hardy
Written in 1940, A Mathematician’s Apology is a love letter to and criticism of the art of mathematics, yes, the art of mathematics. In it, Hardy compares mathematics to poetry many times, and even mathematicians to poets. He says: “A mathematician, like a painter or a poet, is a maker of patterns,” and if that’s not enough to sell you on this beautiful work, perhaps Hardy’s self deprecating take on what mathematicians are really about will peak your interest. I highly recommend this.
3. Any poems by James Sylvester, or maybe even his book The Laws of Verse
Victorian math poet James Sylvester is my personal favorite for the era. His work is what math poetry is all about: making mathematics relatable and human, capturing mathematical beauty in verse, the way we capture other types of beauty in verse, and giving not a single care about it.
4. Modern math poetry!!
I might be biased, but I think the poems my friends wrote are amazing examples of math poetry, read them here: [link]
And another modern creator that I love is 3Blue1Brown on YouTube. Here is a link to his math poetry! [link]
I also have written some math poetry myself, which you can find on this blog in multitudes, but in the spirit of math poetry month and how inspired I was and continue to be by writing math poetry, I want to show you the first math poem I ever wrote. Here is Some Mathematical Love Poetry; for, I don’t know, posterity or something.
Some Mathematical Love Poetry
Kisses are calculus, the examination of limits the jumbled breathing of trapezoids.
Kisses are entropy, nuanced chaos that taste like regulation the systematic rhythm of wanting.
My God, it smells like numbers in here you’ll inhale until only the irrationals are left on account of how dazzling pi appears when reflected in my glasses. Honey,
what would Bernoulli think of us? All lemniscate and no cardioid, proving by induction, holding on in 4-D.
Baby, kisses are algorithms. A step-by-step guide, instructions for the mathematical.
JoAnne, mentioned above, has a great math poetry blog, where she shares some of her work but mostly so many others.
The AMS does some work to support math poetry, including things like this contest.
math problem sheet affirmations. this integral is more scared of me than i am of it
One thing about me is I will always test for convergence
" 'They' isn't singular!" Oh yeah? Show me its multiplicative inverse matrix then.
So I looked up 'singular matrix' because I was paranoid that I'd got the definition the wrong way round, and...
Fucking rude.
Those degenerate singular matrices are destroying our traditional algebraic values of one matrix, one inverse.
Oh, grow up! It's 2023, not all matrices need to have an inverse to have value! Some matrices just want to be in RREF and left alone, have you thought about that?
Plus, it's natural - look at the wild! Non-square matrices have never had an inverse! Your linear algebraic, conservative topology makes me sick.
If you think my topology is conservative, you should see my vector field.
hey. y'all are fucking nerds.
You haven't proven anything there - we took that as an axiom.
[ID: A screenshot of the Wikipedia page for Invertible matrices. "A square matrix that is not invertible is called singular or degenerate. A square matrix is singular if and only if its determinant is 0." The word degenerate is highlighted. End ID]
very sad that the website stopped working because of my fuck up, but since the "random number generator" i scripted was actually supposed to be some sort of poem/conversation between you and the generator, i might as well post the entire text here, also cause barely anyone found it
For those interested, because I've not seen anyone do it, the hexadecimal reads "thank you for reading the stupidest thing i've ever tried to write. the number is 143."
The binary reads "vanilla extract"
The two most important things (higher) math teaches you, IMO, are
how to think carefully about the assumptions of an argument,
that trivial examples of an object are still examples of that object,
where "how to properly define your terms" is an alter-ego of (1).
I'd like to add a bullet (number?): what does it mean to actually prove something
Still similar and closely related to (1), but I don't think it's quite the same!
sorry we applied an operator to your boyfriend. he's an eigenfunction of that operator so the operator returned his function but he's multiplied by a constant. yeah he has an eigenvalue now
BRB, starting a sideblog which reblogs from all those – and only those – blogs which do not reblog themselves.
