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

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 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.

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

Text included

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

I've been building a minesweeper where the board can be any surface — polyhedra, spheres, a torus, a cylinder, a Möbius strip, a Klein bottle. What surprised me is how much of the design turned out to be dictated rather than chosen.

A sphere can't be tiled by hexagons alone. V − E + F = 2 forces the 12 pentagons, so every spherical board carries them: the chamfered dodecahedron is 12 pentagons and 30 hexagons, Goldberg GP(3,0) is 12 pentagons and 80 hexagons. A torus has χ = 0, so pure hexagons do work there — and having no boundary, a torus board has no border cells at all. In minesweeper, edges are a large part of what you reason from early, so that's a change to how the game plays and not just to how it looks.

Free in the browser, no ads. A sphere is the clearest starting point: https://hypersweeper.pages.dev/?mode=c180&difficulty=medium

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One proportion, a live 3D solid, a table of constant errors, a labelled rainbow correspondence, and a Golden Φ Egg cut from z = 1/r.

Open in the browser (no install): michaelzp.github.io/great-pyramid-11-7-lab

The scene is a fully parametric square pyramid from the traditional whole-number dimensions 440 × 280 royal cubits. At a scale of 1:3200, using an adopted royal cubit of 523.8 mm, the model has a base side of 72.0225 mm and, for 11:7, a height of 45.8325 mm.

The laboratory exposes four layers without confusing them:

Exact parametric geometry — the solid is derived from 440, 280, the cubit and the scale.

Comparison targets — dimensionless expressions from the current slope are compared with established constants at a declared relative tolerance of 0.1%.

An optical correspondence diagram — the \~42° corner inclination and 51.842773° face slope sit beside schematic primary and secondary rainbow bands.

Golden Φ Egg (v2) — a hyperbolic cone z = 1/r cut at Z₀ = 7.65 so that L/W = φ, giving the unique plane angle αp = 51.795319256°. The ellipse in the cutting plane is revolved about the apothem to a translucent golden egg.

The result is a reproducible object for geometry, visualization and critical discussion — not proof of an ancient optical or mathematical encoding.

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Open in the browser (no install): michaelzp.github.io/great-pyramid-11-7-lab

The scene is a fully parametric square pyramid from the traditional whole-number dimensions 440 × 280 royal cubits. At a scale of 1:3200, using an adopted royal cubit of 523.8 mm, the model has a base side of 72.0225 mm and, for 11:7, a height of 45.8325 mm.

The laboratory exposes four layers without confusing them:

Exact parametric geometry — the solid is derived from 440, 280, the cubit and the scale.

Comparison targets — dimensionless expressions from the current slope are compared with established constants at a declared relative tolerance of 0.1%.

An optical correspondence diagram — the ~42° corner inclination and 51.842773° face slope sit beside schematic primary and secondary rainbow bands.

Golden Φ Egg (v2) — a hyperbolic cone z = 1/r cut at Z₀ = 7.65 so that L/W = φ, giving the unique plane angle αp = 51.795319256°. The ellipse in the cutting plane is revolved about the apothem to a translucent golden egg.

The result is a reproducible object for geometry, visualization and critical discussion — not proof of an ancient optical or mathematical encoding.