Geometry around us
Instructor: Anna Felikson
Autumn 2022: The notes (hand-written notes in Russian):
- 1. Goat, grass and cabbage: Notes and Turkish Lullaby (3-minutes long cartoon).
- 2. Where to dig a well?: Notes and Combodian Lullaby.
- 3. Illumination Problem: Notes and Lithuanian Lullaby.
- 4. Four Colour Theorem: Notes and Jewish Lullaby.
- 5. Shadows: Notes and Lullaby of Argentina.
- 6. Oranges: Notes and Polish Lullaby.
- 7. Seven Bridges of Königsberg: Notes and Japanese Lullaby.
- 8. Sandwich Theorem: Notes and French Lullaby.
- 9. Paper Snowflakes: Notes and Lullaby of Switzerland.
Resources:
-
4: Four Colour Problem:
- p.290-291 in "What is Mathematics?" by R.Courant and H.Robbins (Russian translation). .
- Chapter 43 in "Mathematical Puzzles and Diversions" by Martin Gardner (Russian translation).
- 5: Shadows:
- How to make a cardboard sundial - instruction, by Inna Pishkina (in Russian).
- 6: Oranges:
-
9: Paper Snowflakes:
- Snowflakes by Jane Kac.
- Mobius hearts by Jane Kac.
- Fractal Christmas Tree by Jane Kac.
- Mathematics with Scissors by Jane Kac (Video in Russian).
- "In one cut" a short article from journal "Kvantik", by Kseniya Pahomova (in Russian).
- A lecture on "Fold and one cut Theorem" by Erik Demaine
Winter 2023: The notes (hand-written notes in Russian):
- 1. Santa's Questions: Notes.
- 2. Map Projections: Notes.
- 3. Braids: Notes.
- 4. Hairy Ball Theorem: Notes.
- 5. Is a mug different from a donut? Notes.
- 6. Euler characteristic: Notes.
- 7. Knots and links: Notes.
- 8. Faces of a simplex and Pascal triangle: Notes.
- 9. Geometry in the corner of the room: Notes.
- 10. Water pouring and billiard table: Notes.
Resources:
- 1. Isoperimetric Problem:
- Dido and Isoperimetric Problem, by I.Sharigin (in Russian).
- 2. Map Projections:
- Mercator Projection, by Andrey Shetnikov (in Russian).
- 3. Braids:
- Braids and Knots, by Alexei Sossinsky (in Russian).
- 4. Hairy Ball Theorem:
- Global wind map, life wind map.
- 5. Is a mug different from a donut?
- Classification of surfaces , by Alexander Veselov (in Russian).
- 7. Knots and links:
- A tale and a song ("A Snail") with string games , by Alexey Andreev (in Russian).
- A string game "A Snail" , instruction by Jane Kac (in Russian).
- 9. In the corner of a room:
- Mathematical fun , book by Boris Kordemsky (in Russian).
- 10. Water pouring and billiards:
- Three jugs problem, translation to Russian from the book "Geometry Revisited" by Coxeter, Greitzer, J. Kvant, 1978.
- Three jugs problem, by im Stevenson (in English).
Spring and Summer 2023: The notes (hand-written notes in Russian):
Resources:
- 1. Playing Dobble:
- 4. Railroad questions:
- Problem by Alexandr Shen, 2min video: Music by Beethoven, words and performance by Alexander Shen (in Russian)
- The curve hidden in plain sight...no flat Earth. Vanishing point of parallel lines, 1min video by Jos Leys (in English).
- 5. Finding treasure:
- J.S. Bach - Crab Canon on a Möbius Strip, 3min video by Jos Leys.
- Music on a Clear Möbius Strip - Numberphile, by Marcus Du Sautoy, 12 min video.
- 6. Mad Tea Party:
- Times Tables, Mandelbrot and the Heart of Mathematics, 13min video from Mathologer, by Burkard Polster (in English).
- 7. Playing Set:
- Playing Set, 15min video by Alexey Savvateev - includes demonstration of big collection of cards without SET and open problems (in Russian).
- 8. Group theory in the bedroom:
- Group theory in the bedroom, by Brian Hayes.
- 9. Numeral systems:
- Numeral Systems, by I.M.Yaglom (in Russian).
Geometry textbook:
- Geometry textbook by O. V. Pogorelov: in Ukranian and in Russian.