mike | Shared With: Everyone - May 10 2008 | math, puzzles
Really interesting problem in recreational mathematics - try to reverse a unit line segment via translations/rotations - but in doing so sweep out a minimal area.
PI/4 is the obvious minimum - but it turns out you can do so in an arbitrarily small area.
What's odd to me, is that any combinations of moves that are either a) rotations about the center and b) translations, CAN NOT achieve an area less than PI/4; so it's counter-intuitive that you can do better than that.
- mike | Shared With: Everyone - May 22 2008 | sudoku, math, group theory, puzzles
There are only 5 billion essentially distinct Sudoku puzzles (solutions) (proof here using Group Theory and Burnside's Lemma).
ShareViewed: 5 Times - mike | Shared With: Everyone - May 11 2008 | sudoku, math, puzzles, programming
Interesting article on rating the difficulty of Sudoku's and various solving methods (including a short backtracking program written in Ruby).
ShareViewed: 19 Times - mike | Shared With: Everyone - May 22 2007 | math, set, puzzles
Cool proof of the largest number of set cards that contain no "SET".
ShareViewed: 16 Times - mike | Shared With: Everyone - Dec 22 2006 | books, math, problem solving, polya, puzzles
The classic problem solving text - Microsoft gave us a copy of this book when we first joined in 1983!
Quoted: Amazon.com: How to Solve It: A New Aspect of Mathematical Method (Princeton Science Library): Books: G. Polya by G. Polya
ShareViewed: 2 Times - mike | Shared With: Everyone - Dec 22 2006 | math, puzzles, problem solving
Favorite web site of Eric C - told me about it in our MIT interview this morning.
ShareViewed: 6 Times - mike | Shared With: Everyone - Oct 18 2005 | Sudoku, Puzzles, Math
Research paper explaining the computation of the number of unique Sudoku grids (accounting for the equivalence relations from renumbering, permutations, and transposition).
ShareViewed: 3 Times - mike | Shared With: Everyone - Oct 18 2005 | Sudoku, Puzzles, Math
Wikipedia entry on Sudoko has summary of solving techniues and counting of unique Sudoku.
ShareViewed: 1 Time - mike | Shared With: Everyone - Oct 18 2005 | Sudoku, Puzzles, Math
Catalog of all known Sudoku with a minimun number (17) of hints.
ShareViewed: 2 Times
- darrellp - May 11 2008
- mike - May 11 2008
- royleban - May 13 2008
You must be Mike's friend before you can comment on this Fave.They actually can sweep out less than PI/4 if they sweep over the same area twice and therein lies the key. Details at http://www.darrellplank.com/math/Besicovitch/Besicovitch.aspx.
Cool. The pictures really help - thanks for creating this page.
Fascinating problem and solution! Very counter-intuitive.
Send Mike a friend request or a personal message instead.