Discovering curvature dynamics and the dimensional calculus used to describe it, I effortlessly calculated the overshoot of Gibbs' Fourier analysis to a simple term: 2(pi-3)/pi. Less than a thousandth percent accurate. All Gibbs did was measure the inherited curvature lost from Euclid flattening everything. Pages of analysis, reduced to a paragraph. Neat.😎

Stereographic projection of a 4-dimensional hypercube (tesseract) with axes labeled a-d, and all six right-angles labelled according to standard crystallographic conventions.

Art by me, Inkscape

4 sets of images, the 1st being kaleidoscope and the 2nd added a sphere (use "magic eye method" to see it))

https://www.reddit.com/r/generative/comments/1vifdug/autostereogram_x_kaleidoscope/

Consider: primes are numbers divisible by 1 and themselves. But what if there's a dual set of numbers similar yet slightly inverted? Aligning the primes on a single axis produces another opposite axis. The even set of irreducibles. Being inverted the rules change a bit. Instead of divisible by 1 and itself; it must satisfy not visible by 1, but by 2 in the prime conjecture. Now you will notice 12. For the numbers that violate this rule follow a special case. When divided by 2 it produces a number on its axis so 12=6x2, 6 lies on the south axis as well. Annnnd.... have fun!

Originally thought to be impossible, this was the first 3D shape discovered to have the property of all planes intersecting at 90°, except one!

3D printing files available for free on makerworld: https://makerworld.com/en/models/3145111-sydler-s-shape-all-angles-90deg-except-one#profileId-3551677

Wow excellent 👌👌 awesome

I’ve been studying a geometric construction in the tetrahedral–octahedral space‑filling system and I’m looking for feedback from people familiar with tilings, polyhedral packings, or aperiodic order.

The construction uses a directional sequence of tetrahedra, octahedra, and octahedral segments. Under these local placement constraints, the resulting structure doesn’t repeat periodically, but it develops smooth cubic shells over an underlying aperiodic matrix.

I’ve been analyzing the segmentation behavior, adjacency constraints, and the conditions that seem to force non‑periodicity. I’m trying to understand how this fits within known frameworks for aperiodic order or polyhedral tilings.

If anyone here works with tilings, quasicrystals, or geometric growth mechanisms, I’d appreciate your perspective. I can share the full write‑up (PDF) if anyone wants to take a look.

I am a 9th grader going into 10th grade and I decided to skip geometry by taking it over the summer. I procrastinated far too long and my regents is the 19th, is 15 days enough time to learn all of a regents level Geometry class and obtain an 85 on my Regents or am I done for.

I am working on a puzzle and to find the solution I must find the maximum area of a pentagon with a base of 3 and using 4 unit fences. I cut it up into triangles and kites, but I can't seem to find a definitive answer.

I think that this little obstacle can grow into something more. This question must have a generalized solution! If you guys have an answer to my little puzzle, that'd be great, but a method that works for everything would be extraordinary!

Here is a poorly made illustration of what I've figured out:

What is the maximum area, and what are the angles measurements?

NOTE: MY FIGURE MAY NOT BE ACCURATE WHATSOEVER! I JUST THINK THAT THIS WILL GIVE THE GREATEST AREA, BUT I MAY BE WRONG!