Links: Below you will find the materials of the courses: there are slides of the workshops (including questions and solutions), in Russian, and links to additional materials on the topics.
- Geometric Orchestra, 2025 (16 hours)
Topics: Pell's equation, Markov triples, hyperbolic geometry, Conway-Coxeter frieze patterns...
- Japanese Temple Geometry, 2023/24 (32 hours)
Topics: Tranditional Japanese mathematics (sangaku), Descartes circle theorem, Apollonian circle packings...
- Geometry around us, 2022/23 (29 hours)
Topics: 4 colour problem, illumination problem, ham sandwich theorem, hairy ball theorem, billiards, topology, Pascal's triangle...
- Geometry in Figures, Geometries, How to solve it? 2022/23 - all under the same link, scroll down
| Topics: | | geometric constructions, conic sections; |
| | inversions, spherical and hyperbolic geometries, 4 dimensions, tilings; |
| | proof techniques: pigeonhole principle,
proof by contradiction, induction, extremal principle, invariants, semi-invariants |
- Mathematics and Art, 2022 (10 hours)
Topics: tilings, fractals, projective geometry, hyperbolic geometry, regular polyhedra, golden ratio, aperiodic tilings...