Geometric Kaleidoscope
Instructor: Anna FeliksonSpring 2026: The notes (hand-written notes in Russian):
- 1. Numerology of 2026 (and constructibility with ruler and compass): Notes
- 2. British flag theorem: Notes
- 3. Catalan numbers: Notes
- 4. Ruler and compass constructions on the sphere - regular polytopes: Notes
- 5. Conic sections 1 - optical properties of ellipse, parabola and hyperbola: Notes
- 6. Conic sections 2 - Dandelin's speres: Notes
- 7. Happy numbers: Notes
Resources:
- 1: Numerology of 2026 (and constructibility with ruler and compass):
- Find the factors blog by Iva Sallay
- How to Trisect an Angle with Origami - Numberphile video with Zsuzsanna Dancso
- Angle trisection using origami, article by David Richeson (construction with the proof)
- 2: British Flag Theorem:
- The British Flag Theorem video by James Grime (on singingbanana)
- Follow-up: British Flag Theorem video by James Grime (on singingbanana)
- 3: Catalan numbers:
- Catalan numbers by Martin Gardner (translated to Russian for Kvant magazine by A.Vainshtein and E.Chernyak)
- Catalan numbers - Numberphile video with Sophie Maclean
- Catalan addendum by Richard P. Stanley - lists many interpretations of Catalan numbers.
- 4: Ruler and compass on the sphere - regular polytopes:
- Dodecahedral calendar for 2026 by Zhenya Kac
- Construction of dodecahedron Euclids' Elements, Book 13. Online edition, by David E. Joyce
- 5-6: Conic sections:
Standard Geometry Textbook:
- Geometry textbook by O. V. Pogorelov: in Ukrainian and in Russian.