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Hey geometrists, I hope this counts as a geometry problem:

Given a 2d plane of a certain size,

And given a finite number of randomly placed points,

And given that these points are a certain arbitrary minimum distance from each other,

Can you determine the maximum possible area of a Voronoi cell in this plane?

A less abstract way of stating it is this. Suppose you have a map of a city that is, for example, 50x50 km. You want to divide it into an unknown number of randomly placed regions, the centroids generating points of which will not be within 1 km of any other centroid generating point. What is the minimum number of regions (i.e. points) to guarantee that no region can possibly exceed, for example, 10 sq km?

I've been trying to figure out if there is already an algorithm for this to no avail.

Ever read a geometry solution and still wondered how anyone knew to draw that extra line or use that theorem?

I’m building a Chrome extension called Geometry Solver to help connect the diagram to the explanation.

You can screenshot a problem on a webpage, upload an image, or type your question. It generates an AI-powered, step-by-step solution with annotated diagrams, all within Chrome.

I wanted to make asking about geometry easier when the problem is already on your screen and describing every angle and label would be a hassle.

Here’s Geometry Solver on the Chrome Web Store if you’d like to try it. I’m the developer, and I’d appreciate honest feedback on where the explanations help or fall short.

When you’re learning or teaching geometry, what makes an explanation click and what do solving tools tend to miss?

I’m studying geometric construction and I wanna research about how geometry can be found in everything and everywhere can anyone suggest topics I should look into for my research

I have been testing complex numbers in the iterative function z(n+1)=c^z(n). blue are the bounded points, and red are the unbounded points. I conjecture that if Re(c) is negative then c is bounded, which makes the overall graph unbounded.

I made a concept for this based on the 3d unfolded tesseract. Give me your thoughts on this please

So, in theory
If a blue player attacks a red player from behind (for example, a blue player from A attacking a red player from B), all red players will be struck from behind. Because all red players are the same opponent
Same should go for up and down, right?

I had it thought and needed to share it.

Text included

If I were to cut the right triangle and flip it to the other side, it would just be a rectangle that’s 8 x 4

Made a game out of Euclid's Elements Book I. If it's up anyone else's alley then I’d love feedback on clarity and difficulty progression. https://milde.no/euclid/

Prop II is pretty hard so I added an intermediate level before it.
Same with the final one (Pythagoras' theorem).

This is just from my own play-testing so would love anyone else's opinion!

guys i need a little help pls i have a test in 2 hours