Batch 2 - Class 25 - Planar Geometry and Tiling

• Let kids demonstrate their App Inventor homework projects - Hriday came with a Pacman game, and Aastha with "No texting while driving"

• MC Diaries Y1, Chap 9 - Warm up 2 - Think of a quadrilateral which can be divided into three triangles with a single straight line cut (Answer: Arrow figure)
• MartinShCol 5.1 - each of two sides of isosceles triangle is one unit long. Without using calculus, find the length of the third side to maximize the triangle's area (Answer: right angle triangle)
• Derived from MC Diaries Y1, Chap 9. Problem Set Problem 3 - Cut a square into n squares for n = 6,7,8,9...

• Periodic Tiling, example square or hexagon - Show MC Escher tilings from web - Ask kids to draw periodic tiling
• Non-periodic Tiling - Ask kids to draw 4 sphinx inside a sphinx - show the tiling

  Spiral Tiling (Heinz Voderberg)
• Penrose Tiling - can be strictly non-periodic. Golden Ratio (1.618...)

  Make actual penrose tilings using Kites and DartsShow how Penrose Kites and Darts can also apply to arbitrary shapes like chicken
• Practical applications of Penrose Tilings

  Quasicrystals have a pattern similar to Penrose Tiling and are non-repetitive; they are extremely resistant to wear and tearKleenex used penrose tiling on their quilter toilet paper, so that the toilet paper won't bunchAnticipated parallels to quantum mechanics and hyperdimensions

• Four towns at four corners of a square. how should they be connected to minimize length of railroad (hint: not diagonally - Its 1+sqrt(3) - essentially two three pointed stars with center of towns as meeting point - 120 degree at star) - interesting demonstration https://www.youtube.com/watch?v=dAyDi1aa40E - Steiner points (but they break down due to local minima)