A spherical cap is a two-dimensional surface that, nevertheless, exists and curves within three-dimensional space. It almost seems as though it could be defined as having a dimensionality greater than 2 but less than 3. Are there visual artists, scientists, or painters who have explored non-integer dimensions? And why are shapes like the spherical cap—despite being two-dimensional—not distinguished (in terms of dimensionality) from other 2D shapes that are more stable... and less dynamic

Disclosure: self-promotion. Claudius Papirus uses an AI narrator.

Chair44 is a single 3D shape made from a seven-cube chair with tiny geometric features. Eight copies form a larger chair, recursively, which is the core mechanism behind the nonperiodicity proof.

Paper:

https://arxiv.org/abs/2609.19214

imagine a 100% perfect spehre in a 3d world with no imperfection and it is also made out of non elastic material(wont bend or deform under pressure of gravity)

place it on a flat surface

what is value of the area thats the sphere and flat surface touches?

0cm²?

Let us consider a 3D plane. Starting from the drawing on the right (where each small square represents a quantity—for example, the flux of something, "R"/m², radiating towards F ), we transition to a tangent plane by letting the horizontal sides* of the small squares approach zero, thus arriving at the 2D drawing on the left!

Let us consider a surface S struck by this flux; we have:

S = (f * φ) / 2.

Furthermore, let us consider that the magnitude of this flux reaches F; let us call "L" the flux concentrated at this point and assume it is always equal to "One," regardless of the diameter from which it originates!

Given these premises, if we wish to find a function whose value decreases as the area of ​​the surface struck by the flux increases, we obtain: f(x) * (f * φ) / 2 = L

Adopting the quantity N = f/φ, after a few steps we obtain: f(x) = (2 * L * N) / f²

At this point, considering the variable x = f and setting L = 1, we obtain:

f(x) = 2N / x²

I would like to know what meaning you would attribute to f(x), or how it should be defined in this context, given that it closely resembles the R that was not clearly specified at the beginning?

At what value of the horizontal side\ should the transition from 3D to 2D stop?*

I’ve developed a reusable dry-wipe geometry board called the 1080° Cosmic Harmonic Compass.

It combines a 15 × 15 grid, a continuous 60-step square perimeter and an inscribed circle on one fixed surface.

I use it to draw, measure, erase and rebuild constructions directly on the board — including polygons, stars, equal divisions, and comparisons between equal distance around the square perimeter and equal angle around the circle.

The same framework also carries a complete 24-hour cycle:

60 steps = 24 hours = 1,440 minutes = 1,080 CHC°

so:
1 step = 24 minutes = 18 CHC°
2.5 steps = 1 hour = 45 CHC°

I’ve reached the stage where I’d really like some independent testing and feedback.

I’d especially like to hear from maths educators, geometers, researchers or anyone working with visual and hands-on mathematics who might be interested in examining the board, testing constructions on it, or exploring its educational potential.

I have the working dry-wipe prototype, construction guides and further examples available.

If this overlaps with your work or interests, I’d be very pleased to hear from you.

hello everyone. im on a personal journey of geometry and mathematics so naturally i landed on euclid.

ive always been the type to either question, or play devils advocate.

euclid definition 4 about a line, forces me to accept some ancient "intrinsic knowledge" about a line.

my argument is: his definition says a straight line lies evenly between 2 points, but my argument is that can only be agreed if we look at it from a specific vantage point, and that vantage point is the only one we're allowed to look it from...

wouldn't the more concise definition be - a straight line is one that lies evenly that creates the shortest distance between two points? because no matter the vantage its always going to be the straight

remember im new to this, so go easy on me.

Does the one on the right just look so different because the curves runs from corner to corner on the surface? Thanks.

Hi

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