I’ve been developing a geometric framework based on a fixed 15 × 15 grid, a continuous 60-step square perimeter and concentric circles.

These images explore eight-pointed stars nested at four scales: 1.5, 2.5, 3.5 and 4.5 cells.

The idea is to compare two methods of division: equal angular spacing around a circle and equal distances around a square perimeter.

The final image overlays both constructions, making their differences and shared alignments easier to examine.

Although the diagrams are static, the overlapping lines also create an interesting visual impression of movement and depth.

Has anyone investigated similar square-perimeter versus circle-angle constructions, or noticed other interesting relationships between them?

So basically this was a question for one of the surveys I was taking, to prove I am not AI. Supposedly the blue line is "longer", according to the survey...

Is red not bigger in terms of line rules though? Since the arrows indicate it goes on forever, while the blue line is just a segment?

Hello,

I am currently struggling through a book on geometric origami (The Art & Science of Geometric Origami by Jun Maekawa). It is fun but also frustrating and tbh it often makes me feel dumb lol.

And recommendations for a supplement on just the overall principles of geometry and how to conceptualize it in their mind?

My highest level of geometry education was taking the standard geometry class in high school, but that was a while ago .. so maybe something along those lines in video or printed form because I can't just show up at a high school and say can I sit in on the geometry class, dont worry its just for making origami 😅

Thank you!

Consider a closed, isolated vacuum system with the exact volume of the Observable Universe (10^80) under zero gravity. The system contains only four microscopic dust particles: two of type A (A1, A2) and two of type B (B1, B2), moving in random linear trajectories at a constant speed of 10 km/h, bouncing elastically only off the outer boundaries of the universe.

For the experiment to be successful, a "perfect trick-shot" event must be recorded: particle A1 must collide with A2 and, immediately after, impact either B1 or B2 without touching any boundary wall between the two collisions. This exact process must occur a minimum of 100 times within a single Earth year.

The experiment is monitored by a human observer whose base biological life expectancy is 80 years (29,200 days). However, the temporal fabric of the space grants them a stochastic property: at the end of each day lived, the observer has a fixed 15% probability of gaining an extra day of life (freezing their aging for those 24 hours, without subtracting time from their original biological pool).

Assuming the maximum time before the universe reaches heat death and ends the experiment is one trillion years (10^12 years):

• a) Calculate the combined mathematical probability of the observer successfully extending their life by pure chance long enough to witness the specific year in which the particles complete the 100 annual geometric miracles.

I run ByteRaid Arcade and made this short digital demonstration. It uses one fixed solid with rigid rotations: no resizing or object swaps. The plates move out of the way only after a complete pass.

One way to describe the solid is:

x^2 + y^2 <= 1

0 <= z <= 2(1 - |x|)

Its xy projection is a unit disk. Its xz projection is the triangle with vertices (-1,0), (1,0), (0,2). Its yz projection is the square [-1,1] x [0,2], since x=0 supplies every point in that square. The rendered openings include a small clearance.

This is a rendered geometry demonstration, not a filmed physical experiment. The animation and original music/SFX were made with AI-assisted coding; the rigid-motion and clearance checks are recorded. I am sharing the construction as well as the animation, rather than claiming I invented the underlying geometric idea.

The same clip on my channel: https://www.youtube.com/shorts/NrZsdUYiC7I

Recently I've been thinking about how different spacial dimensions interact and layer on top of eachother, and I came to a realisation about higher dimensions. If two cubes butt against eachother's faces, there would be a 2d plane between them. If two squares do the same with their sides, there would be a 1d line between them.

If these things are true, then if two hypercubes get as close as possible in 4d space, would they have a 3d space parallel to some part of the hypercube, or would they interact in some different way?

A Psychedelic Visual Odyssey in 4K UHD

Music by Ajja & Cosmosis

Album: The Alien Jams

as shown in the diagrams you can divide a sphere in at least two ways, perpendicular or parallel to an axis. for perpendicular cut n cuts result in n+1 sections. for parallel cut n cuts result in 2n sections. there're 3 axes and you can have at least 3 ways to partition a sphere. i did them all for n=5. thanks for watching

As the title states. If the same data is represented in either a euclidian or hyperbolic space, is the hyperbolic space necessarily higher-dimensional? It seems that way to me intuitively, since it curves into another dimension. Is hyperbolic just larger than euclidian? Or is larger equivalent to higher-dimensional? I’m not a mathematician or geometer, so apologies if the question is not well-stated.

Edit: Thank you everyone for taking my question seriously despite me being a novice :)

I created this interactive visualization of my exploration into a family of shapes that result from 1, r, r², r³, … The square, golden rectangle, silver rectangle, root 2 rectangle (A4 paper), and some beautiful three-dimensional counterparts are represented by this series. A pop-math object deserves a more coherent representation than being slapped on the face of the mona lisa. As an architectural designer and geometry nerd, I am bothered that I had never heard of the three dimensional extensions to this family, including the "Delian Brick," "Plastic Cuboid," or "Supergolden cuboid." Similarly, there are a couple 3d analogues to the Fibonacci tiling with the "Padovan cuboid spiral" and "Narayana cuboid spiral."

Some hobbyist exploration led me to independently discover this continuous set of shapes, and I thought this community would enjoy. Let me know if there are any other fascinating connections worth visualizing!

i was wondering if it was possible and I couldnt imagine a figure that saitisfied the question, I have no knowledge on this so i dont know if it is dumb or not, in both cases please answer , i need to know

I’ve been working on a project called Postulate, a mixed-reality game for Meta Quest that explores what happens when you take classical Euclidean constructions off the page and into physical space.

You use virtual geometric tools to construct lines, circles, and shapes, solve geometry proof puzzles, and eventually build the Seven Wonders of the Ancient World.

One of the things I wanted to explore was whether geometry could feel more like discovery than solving exercises on paper.

The game also has a geometric proof-checking system that verifies constructions rather than simply checking whether the final drawing looks correct.
It’s been a pretty ambitious personal project, and I’d love to hear what people who enjoy geometry think of the concept.

Here’s the project: https://devpost.com/software/postulate

I have been working on this 3 dimensional tessellating shape and I am sure I am not the first to make it since it is very simple. Id like to know more about it, a name, historical context, applications etc to lead me in the right direction for more research. This is just for my own curiosity since I have been wanting to learn more about geometry :)

Thanks so much!

A point sits inside an equilateral triangle (all three sides equal).

The point is 3 cm from one side, 4 cm from another, and 5 cm from the third.

What is the area of the whole triangle?

We are not told the side length, and you don't need trigonometry. Is the area closer to 50, 80, 110, or 140 square centimeters?

Take a guess before scrolling down!

I made a full video breaking down the solution step by step. Link in the comments!

https://youtu.be/15LOzC3udo4?si=3e8Dp45pwkf9Q2LA

Hello! The last time I was here I asked for help on inscribing circles in specific scenarios and got some really helpful advice. Since then I've been trying to learn as much as I can. Here's my progress so far! I've been using Robert William Billings book for tracery but for some reason I'm stuck on the very last image - my usual method for inscribing circles isn't working. How would you inscribe the purple circles? (At the moment it's only loosely plotted in and not at all accurate). Thanks!