geometry

name	geometry
description	Shapes, spaces, and spatial relations
license	MIT
compatibility	opencode
metadata	{"audience":"mathematicians","category":"mathematics"}

What I do

• Analyze Euclidean geometry and proofs
• Calculate areas and volumes of geometric shapes
• Apply trigonometric relationships
• Work with conic sections (ellipse, parabola, hyperbola)
• Use coordinate geometry and transformations
• Apply non-Euclidean geometry concepts

When to use me

When solving spatial problems, geometric proofs, or coordinate system calculations.

Key Concepts

• Pythagorean Theorem: a² + b² = c² for right triangles
• Area Formulas: Triangle = ½bh, Circle = πr², Sphere = 4πr²
• Trigonometry: sin²θ + cos²θ = 1, law of sines, law of cosines
• Conic Sections: Circle, ellipse, parabola, hyperbola from plane intersections
• Transformations: Translation, rotation, reflection, scaling
• Vector Cross Product: |a × b| = |a||b|sinθ gives area of parallelogram