Differential Geometry
Explore curves and surfaces; metrics and curvature; manifolds and forms. Concepts and connections are available independently of video coverage.
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Coordinate geometry
Coordinates translate geometric conditions into equations and algebraic calculations.
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Angles
An angle measures rotation between rays sharing an endpoint.
Distance formula
Euclidean distance is the square root of the sum of squared coordinate differences.
Polyhedra
A polyhedron has polygonal faces meeting along edges and vertices.
Regular curves
A regular curve has a nonzero velocity, allowing local tangent geometry.
Regular surfaces
Regular surface charts have linearly independent coordinate tangent vectors.
Knowledge connections
- Distance formula · Related · Map context
- Rigid motions · Related · Map context
- Angles · Related · Map context
- Polyhedra · Related · Map context
- Distance formula · Next concept · Map context
- Regular curves · Related · Map context
- Smooth manifolds · Related · Map context
- Regular surfaces · Next concept · Map context
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Geometry
Explore plane geometry; coordinates and transformations; space and geometry beyond euclid. Concepts and connections are available independently of video coverage.