Geometry. Lecture 1
2026LectureФёдор Попеленский
What geometries there are and what they have in common — Klein's Erlangen programme; the school 3–4–5 triangle and the ellipsoid; the cube and the brick as finite geometries; metric spaces; groups, quantifiers in the axioms; the group of bijections and the order of composition; left and right actions of a group on a set; the metrics , , on ; isometries, subgroups; the order of an element; orbits, stabilisers, transitive actions; the list of geometries in the course — the Euclidean plane, the regular triangle and , the cube and its 48 symmetries, the Poincaré model of the Lobachevsky plane; fundamental domains; subgeometries — the square in the cube.
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