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△ Geometry

Sources: wpWikipedia (CC BY-SA 4.0) · june.kim (CC BY-SA 4.0).

From Euclid to curvature. Runnable code, SVG diagrams, plain English.

A B C Triangle inscribed in its circumscribed circle.
Chapter
1. Euclidean Geometry Five axioms, compass and straightedge, and the theorem that launched a thousand proofs △
2. Coordinate Geometry Descartes put numbers on geometry: distance, slope, lines, and conic sections △
3. Transformations Translate, rotate, reflect, scale — and discover that symmetries form a group △
4. Projective Geometry Add points at infinity so parallel lines meet, then watch points and lines swap roles △
5. Non-Euclidean Geometry Drop the parallel postulate: on a saddle there are many parallels, on a sphere there are none △
6. Differential Geometry Curves bend, surfaces curve, and curvature is a number you can compute △
7. Metric Spaces Distance functions, open balls, and metric spaces as enriched categories △
8. Convex Geometry Convex sets, convex hulls, separation theorems, and Minkowski sums △
9. Voronoi Diagrams Nearest-neighbor partitions, Voronoi cells, and Fortune's algorithm △
10. Delaunay Triangulation Dual of Voronoi, circumcircle property, convex hull in one higher dimension △
11. Power Diagrams Weighted Voronoi diagrams and the geometry behind ad auctions △
12. The Erlangen Program Klein's insight: a geometry is defined by its symmetry group △

📺 Video lectures: MIT 18.900 Geometry and Topology

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