Geometric Orchestra

Spring 2025: The notes from rehersals (hand-written notes in Russian):

• 1. Numerology of 2025 (triangle and square numbers)
• 2. Chromatic number of the plane
• 3. On Kangaroo... (Chromatic number of the circle)
• 4. Pell's equation
• 5. Markov's triples
• 6. Markov's tree (and other trees and numbers)
• 7. Hyperbolic geometry: lines
• 8. Hyperbolic geometry: isometries and triangles
• 9. Hyperbolic geometry: Tilings. (Sperical Coxeter polygons)
• 10. Hyperbolic geometry: Tilings. (Euclidean and hyperbolic Coxeter polygons)

Resources:

• 1. 343867 and Tetrahedral Numbers Numberphile video with James Grime
• 2. Chromatic numbers Andrey Raygorodsky (Notes of Lecture for school students, in Russian)
• 3. Kangaroo Question (a poem by myself, in Russian)
• 4. V. Bugaenko Pell's Equations (notes of 2 lectures for high school students, in Russian)
• 4'. V. Senderov, A. Spivak Pell's Equations - and part 2 and part 3 by A. Spivak (articles in "Kvant Journal", 2002, in Russian).
• 5. M. G. Krein, Markov's Equation (article in "Kvant Journal", 1985, in Russian).
• 8. Tilings by (and after) Escher. Webpage on Mathematical Imagery by Jos Leys.
• 10. Make Hyperbolic Tilings of Images. AppletMake Hyperbolic Tilings of Images by Malin Christersson.

Standard Geometry Textbook:

• Geometry textbook by O. V. Pogorelov: in Ukranian and in Russian.

Links to 2022-24 pages:
        Japanese Temple Geometry
        Geometry Around us
        How to Solve it - and - Geometry in Figures
        Mathematics and Art

The webpage uses the following paintings:
    Left: Georges Braques, "Musical Forms", 1918.
    Right: Pablo Picasso, "Guitar", 1913.