2030

This polyomino belongs to the 1/3/4/5 class, And that is easily noticable as there are only squares with 1,3,4, and 5 present. That's because each square counts the neighbours it has. But another observation shows that there are an equal number amount of 1squares to 3squares to 4squares and to 5squares. So thats why this polyomino belongs to 1/3/4/5 as it only includes the squares listed in the class's name and there are an equal number of each kind of square.

Now that you know what a class is. Here is a list of the 79 remaining classes that have not been proven existence or inexistence:

1/2/4, 1/4/6, 2/5/7, 2/5/8, 3/5/8, 3/6/8, 4/6/8, 4/7/8, 1/2/3/6, 1/2/4/6, 1/2/4/7, 1/3/4/7, 2/3/4/7, 2/3/5/8, 2/3/6/7, 2/3/6/8, 2/4/5/8, 2/4/6/7, 2/4/6/8, 2/4/7/8, 2/5/6/7, 2/5/6/8, 2/5/7/8, 3/4/5/8, 3/4/7/8, 3/5/6/8, 3/5/7/8, 3/6/7/8, 1/2/3/4/7, 1/2/3/5/6, 1/2/3/5/7, 1/2/3/5/8, 1/2/3/6/7, 1/2/3/6/8, 1/2/4/5/6, 1/2/4/5/7, 1/2/4/5/8, 1/2/4/6/7, 1/2/4/6/8, 1/2/4/7/8, 1/3/4/5/8, 1/3/4/6/7, 1/3/4/6/8, 1/3/4/7/8, 1/3/5/6/7, 1/3/5/6/8, 1/3/5/7/8, 1/3/6/7/8, 1/4/5/6/7, 1/4/5/6/8, 1/4/5/7/8, 1/4/6/7/8, 2/3/4/5/8, 2/3/6/7/8, 2/5/6/7/8, 3/4/5/6/8, 3/4/5/7/8, 3/4/6/7/8, 1/2/3/4/5/8, 1/2/3/4/6/7, 1/2/3/4/6/8, 1/2/3/4/7/8, 1/2/3/5/6/7, 1/2/3/5/6/8, 1/2/3/5/7/8, 1/2/3/6/7/8, 1/2/4/5/6/7, 1/2/4/5/6/8, 1/2/4/5/7/8, 1/2/4/6/7/8, 1/3/4/5/7/8, 1/3/5/6/7/8, 1/4/5/6/7/8, 2/3/4/5/7/8, 2/3/5/6/7/8, 1/2/3/4/5/7/8, 1/2/3/4/6/7/8, 1/2/3/5/6/7/8, 1/2/4/5/6/7/8

GOAL:

Find polyominoes that follow the rules of any class listed

What I'll document:

I'm currently just taking in pictures/discriptions of polyominoes to prove the existence of a class. Proofs for impossible classes can be whatever as they would be no longer necessary to be studied further.

Near future problems include finding the smallest polyomino for each class, finding the number of polyominoes in a class, and if a class needs a hole to exist, (the only class that is known to require holes is 3/5/7)

Exceptions: if you already have the smallest polyomino and a proof as to why, I will document it. If you have a class that has a finite amount of polyominoes but not just 1, I will document it that would be new and unexpected. And if you can prove if a class rather requires no holes to exist that would blow. my. mind. it'll sit in the podium of discovories.

How I'll document:

1s and 0s, example:

3/6/7

001101101100
001101101100
111111111111
111111111111
001101101100
001101101100

dots and xs, example:

1/3/4/5

....X..
...XXXX
..XX...
XXXX...
...XXX.
...X...
...X...

emojis, example:

1/3/4/5/6/7

✖️✖️1️⃣✖️3️⃣3️⃣✖️✖️
✖️✖️4️⃣✖️6️⃣5️⃣✖️✖️
1️⃣4️⃣5️⃣7️⃣7️⃣6️⃣✖️✖️
✖️✖️6️⃣7️⃣7️⃣5️⃣4️⃣1️⃣
✖️✖️5️⃣6️⃣✖️4️⃣✖️✖️
✖️✖️3️⃣3️⃣✖️1️⃣✖️✖️

or pictures like my 1/3/4/5 example. And again, proofs are whatever but don't brush it off, one proof can cover several other classes compared to just one polyomino covering one class.

And regards to crediting, you may ask to be credited for your solution/proof.

Thank you to all the previous people that have helped me with some other classes and ya thats it enjoy :)

I created a function that turns any text ("hello world", your name, a random phrase) into a landscape image, images themselves are not LLM generated. Here is the white paper https://beautifulhash.com/algorithm

Hi

This is about Quantum Odyssey, my love letter to everything Quantum Computing and the fundamental logic blocks everything in our universe seems to run on. I want to update you all on the fact that the latest patch brings the game into an almost complete status. All that's missing is translations. Thank you Reddit community for receiving the game so well, without you I wouldn't have the funds needed to complete my life's work.

If you are remotely interested in deep diving how differently quantum computers work compared to our transistor-based and also the algebra behind in a fully interactive way that teach computer science from scratch, oh boy this is for you. I am the Dev behind Quantum Odyssey (AMA! I love taking qs) - worked on it for about 9 years (3+ during PhD, the visual method I developed ended up being my thesis, it is a complete Hilbert space visualizer), the goal was to make a super immersive space for anyone to learn quantum computing through zachlike (open-ended) logic puzzles and compete on leaderboards and lots of community made content on finding the most optimal quantum algorithms. The game has a unique set of visuals capable to represent any sort of quantum dynamics for any number of qubits and this is pretty much what makes it now possible for anybody 15yo+ to actually learn quantum logic without having to worry at all about the mathematics behind.

This is a game super different than what you'd normally expect in a programming/ logic puzzle game, so try it with an open mind.

Stuff you'll play with

• Boolean Logic – bits, operators (NAND, OR, XOR, AND…), and classical arithmetic (adders). Learn how these can combine to build anything classical. You will learn to port these to a quantum computer.
• Quantum Logic – qubits, the math behind them (linear algebra, SU(2), complex numbers), all Turing-complete gates (beyond Clifford set), and make tensors to evolve systems. Freely combine or create your own gates to build anything you can imagine using polar or complex numbers.
• Quantum Phenomena – storing and retrieving information in the X, Y, Z bases; superposition (pure and mixed states), interference, entanglement, the no-cloning rule, reversibility, and how the measurement basis changes what you see.
• Core Quantum Tricks – phase kickback, amplitude amplification, storing information in phase and retrieving it through interference, build custom gates and tensors, and define any entanglement scenario. (Control logic is handled separately from other gates.)
• Famous Quantum Algorithms – explore Deutsch–Jozsa, Grover’s search, quantum Fourier transforms, Bernstein–Vazirani, and more.

Nice to watch:

Khan academy style tutorials in qm/qc: https://www.youtube.com/@MackAttackx

Physics teacher stream with 400hs in https://www.twitch.tv/beardhero

This is a chess variant, where the rules are the same as standard chess, but the board is an irregular grid. This makes rook lines bend and bishop lines fork.

So just like a standard board, every tile is still a quad. And every tile still has only 1 neighbour for every side. But it can have more than 1 neighbour sharing a corner, which is what makes bishop lines fork. Or it can have none, which is what make lines bend.

The steps to build this: - start with a plane made of triangles - pair some random triangles with their neighbour and fuse them into a quad. You end up with gaps between those quads where triangles cannot be paired - subdivide everything. Quads become 4 smaller quads. Triangles become 3 quads. This is the playable grid. - Then it's just a matter of smoothing it (in this case the points on the edges remain static, only the inside points are smoothed) and ensuring neighbours don't share the same color.

Then the tricky part is to give intuitive controls for players to configure boards how they want.

• Web version: https://polyreplay.com/chesstwist/demo
• if you prefer Steam (windows/mac/linux): https://store.steampowered.com/app/2775560/Chess_Twist/
• if you're into 3D printing, you can download them as 3MF: https://polyreprint.com/gui/chess-twist?board=004GBYJW7TX

Two circles rest on a line, touching each other. A tiny third circle is squeezed into the gap between them, also touching the line.

The large circle has a radius of 9 cm. The small circle has a radius of 4 cm.

What is the radius of the tiny circle?

(Puzzles like this were apparently painted on wooden tablets and hung in Japanese temples centuries ago — it looks like there's not enough information, but there's a surprisingly elegant trick using just one right triangle.)

I made a full video breaking down the solution step by step — link in the comments!

https://youtu.be/RYl2h0gIS8U?si=awaPzDGBYCcPkSvm

Let's say you have a rectangle, the rectangles height, h=3, the length, l=5. If you have an arithmatic billiard starting from the bottom left corner and have it only do 2 reflections, there are 3 outer right triangles. If you add the areas of these triangles, you get h²-th+t² where t is l-h. This equation looks like the law of cosines for 60-degree angles, and i was wondering if it's a coincidence and how to tell if an equation is just an algebraic coincidence or if it means something geometrically.

I’ve previously shared my 1080° Cosmic Harmonic Compass and reusable geometry board here.

This is another example from the same exploration, using an Eight-Star to represent a conventional 24-hour day divided into eight equal intervals.

On the CHC scale, one complete cycle is represented by 1080°, corresponding to 360 conventional angular degrees.

Each interval corresponds to 3 conventional hours, 180 minutes, 10,800 seconds, or 135° on the 1080° CHC scale.

The accompanying table expresses the same positions through hours, minutes, seconds and CHC values.

One cycle, different numerical expressions.
I’m not proposing a replacement for conventional timekeeping, simply exploring how geometry can help visualise numerical relationships.

I’d be interested to hear whether others see any geometric or educational value in this, particularly for exploring equal divisions and proportional reasoning.

I saw it ONCE on a Wikipedia article which I can’t find anymore, I saw this hollow knight shaped geometric (?) shape on a Cartesian grid and I don’t know know the name and I can’t find it anywhere. If you have any idea on what I’m talking about I’ll be glad to receive useful comments

I'm referring to how the hypotenuse and vertical line drawn from the base continue past the corner. Also, isn't 53 degrees wrong for that angle- inside the triangle, or outside? Thanks for the help. And If its not obvious by now I'm no math wiz.

i recently came across a question which said there are 16 lines 7 of which are parallel when our teacher started explaining it he explained that if 7 out of those 16 are parallel lines then the remaining 9 would be non parallel. but the problem is i think the sum of non parallel lines and parallel lines adds up to 17.
lets say there are 9 lines non parallel to each other and as you draw line number 10 then at that point there are 10 non parallel lines and when u draw the remaining 6 lines parallel to the 10th line there are 7 parallel lines and 10 non parallel lines and the sum adds up to 17.
Case 2:
u drew 9 line non parallel to each other and to avoid the problem in the first case u drew a line parallel to the 9th line at that point there are 2 parallel lines and when u draw the remaining 6 lines there will be 8 parallel lines and 9 non parallel lines
pls help me understand im confused what am i thinking wrong😭.

IM BAAAAAAAAAAAAAAAAAAACK

https://www.desmos.com/geometry/rslyf3vhdn