Farrago Of Fragments

Cool proofs, facts, objects

• Roomba -> Euler
• Perrin Sequence, and 1, 2, 4, 8, 16, 31
• Cantor's first proof
• Mutilated Chessboard
• 13 piles of 4
• Non-crossing Euler, both directions
• Pythagoras and general triangle, both directions
• Hamming: 4+3
• High-dimensional spheres are "spikey"
• Tumbling rings
• Spinning Red/Blue tube
• Any rectangle tiled with "half-integer" rectangles is itself a half-integer rectangle

Physics / Calculations

• Tinking tea cups
• Rope around the Earth
• The other rope around the Earth
• Distance to the Moon
• Vertical terminator / horizontal terminator
• Measure c with microwave
• http://en.wikipedia.org/wiki/Lanchester's_laws

Games

• Drommels (via Fred Horn)
• Parallelograms (via Fred Horn)
• Product
• CoNeutron
• X-only TicTacToe

Puzzles

• Assassins
• Circle dissection
• 12 face fully symmetric solid (via Nick or John)
• Flipping Ice Cream cake (via John McLeod)
• Set of sets of N, sum = 20, product maximum
• Four coins to line, six coins to hexagon
• 2 = 4
• Hole in disk : dissection
• Rotation, Reflection, Translation
• 2 of 1 kg balanced
• Peter Higgins' friend's daughter
• Josh's polynomial problem
• 10x10 board, 41 rooks, find five that don't attack
• Maximise volume of cuboid if Length + circumference = 100
• Tile 8x8 with 2x1, is there necessarily a 2x2?
• Three litre, five litre
• 1, 2, 5, 10 minutes - limit of 17
• My oldest plays the piano