Once proved, mathematical theorems* tend to stay proved. Nevertheless, they can sometimes still be improved – say, by making them shorter. Take, for example proofs for The Hairy Ball Theorem. Mathematician Henri Poincaré first drew attention to the Hairy Ball Theorem in 1885 with his treatise ‘Sur les courbes définies par les équations différentielles (III)’ Journal de […]
Tag: math
Improving our understanding of Bamboozle Structures
It’s not everyday that a newly discovered 3-D mathematical concept appears on the topological horizon. But one did in 2012. It’s called the Bamboozle Structure. “Bamboozle consists of 51 equilateral triangles, meeting pairwise at an angle of about 70.5 degrees (arccos 1/3).” It seems that topologists haven’t given a great deal of consideration to Bamboozle […]
The trick of making Sudoku games
The MathWithBadDrawings blog looks at how complicated — or, rather simple — it is to create lots and lots of sudoku games: “Now, I’m not much of a Sudoku player. (Crossword guy, to be honest.) But glancing at the puzzle, my dad and I got to wondering: How do they generate these puzzles? We weren’t sure. […]
Generalizing Keeler’s theorem (a.k.a. The Futurama Theorem)
Theorem 1. Let n ∈ N, n ≥ 2. The inverse of any permutation in Sn can be written as a product of distinct transpositions in Sn+2 \ Sn. Mathematically inclined aficionados of the cult animation series Futurama will no doubt recognise the theorem above – it was first posited by Ken Keeler in the […]