randformblog on math, physics, art, and design |
In an old randform post about solar cells I was writing a bit about the computer modelling of solar cells. In particular I mentioned that it seems that the involved models use mainly a theory which was to a great part developped by Shockley and Queisser in the 50/60s.
I try to stay up to date with what’s going on in the math and physics world by e.g. reading blogs of scientists. One of the probably most famous blogs in the mathematical physics world is this week’s finds by John Baez whom I visited on Friday.
A small update to nad’s post on indra’s pearls: Jürgen Richter-Gebert has made an interactive course (german only) with his dynamic geometry program Cinderella. Now you can easily experiment with those circles and iterated function systems yourself.
Today’s post is about one of the rare examples where probably an artist made a discovery before the scientist did.
another mathematician’s blog on math, music, art, and stuff.
incidentally he is at TU Berlin at the moment…
A regular Rubik’s cube has 43,252,003,274,489,856,000 permutations (different positions) and it is still unknown how many moves are needed to solve the cube, that is to find a shortest path from a given permutation to the trivial one. If you count turning a face as a move it is known that there are permutations that need 20 moves. This is a lower bound meaning that one knows that there are permutaions that need at least 20 moves, but there might even be permutations that need more. Last year the upper bound by Silviu Radu was 27 moves but Dan Kunkle and Gene Cooperman now showed that it can be done faster: With massive computer aid they showed that 26 face moves are enough.
So the situation is: there are permutations that need 20 or more moves and any permutation can be solved with at most 26 moves. The gap of 6 between these two numbers gives us the following bounds: We can expect at least one more paper and at most 6 more papers that reduce the gap.
The above pictured pocket cube has only 3,674,160 permutations and optimal solutions for all of them can be generated by a brute force algorithm.
this is an update to The eighties recycle themselves and rubiks robots.
This year is Euler‘s 300. anniversary. It is Euler year and today is the 15. Euler lecture ( 14:00) at neues Palais in Potsdam.
A remarkable mathematical conjecture (proven 1995 by Sabitov) is that there exists no rigid bellows. This means if you have a closed volume which is formed by (triangle shaped) “plates” and if you deform it then the volume stays always constant (i.e. if it would have been a bellows then you couldnt press air out of it). This is why accordions need some elastic fabric in order to allow for deformation. May be also a useful knowledge for architecture, since it means that if you press a (closed) house on one side it would bulb on some other side.
The workshop Rigidity and polyhedral combinatorics is discussing related problems.
