Geometry MOC
Geometry studies shape, distance, angle, size, and position. It begins with ideal objects such as points, lines, planes, and circles, then generalises to Euclidean spaces, Manifolds, metrics, and Curvature.
Core notes
- Geometry — overview and map of the subject.
- Point — exact position with no size.
- Line — one-dimensional Euclidean geometry.
- Plane — two-dimensional geometry and coordinates.
- Space (3D) — ordinary three-dimensional Euclidean space.
- Area — two-dimensional measure.
- Circle — fixed-distance curve in a plane.
- Trigonometry — angles, triangles, rotations, and periodic functions.
Spaces
- Euclidean spaces — flat spaces with ordinary distance.
- Euclidean spaces index — local map for line/plane/3D notes.
- Curvature — how spaces or curves deviate from being flat.
- Manifolds — spaces that are locally Euclidean but may be globally curved.
- Gravity as emergent from spacetime curvature — bridge from geometry to general relativity.
Learning path
Start with points, lines, and planes, then learn coordinates and vectors. Add the Euclidean metric to measure lengths and angles. From there, Vector Calculus index extends calculus to fields on space, while manifolds and curvature explain what changes when flat geometry is only a local approximation.
Physics bridges
Geometry underlies position, Velocity, Work, Potential energy, and Cosmology index. It is also the visual language behind fields, fluxes, orbits, lenses, and spacetime diagrams.