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Meta question: where can I find list of simple unsolved/undiscovered problems like these in math? It does not appear in https://en.wikipedia.org/wiki/List_of_u
by est 11y ago
Meta question: where can I find list of simple unsolved/undiscovered problems like these in math?
It does not appear in https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_mathematics https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_m...
- jbrooksuk 11y agoI don't think that tiling a plane is exactly a "simple" problem.
- est 11y agoI mean something simple enough to understand, and could be played by average programmer in a IPython Notebook. I didn't mean simple to solve, just lower barrier of entry.
- leni536 11y agoI like this one: http://www2.stetson.edu/~efriedma/squinsqu/ http://www2.stetson.edu/~efriedma/squinsqu/ Can be easily generalized to other shapes and more dimensions too.
- pavel_lishin 11y agoDoes the lack of n = 16 mean that there's no current proof?
- leni536 11y ago> For the n not pictured, the trivial packing (with no tilted squares) is the best known packing.
- Dylan16807 11y agoWhy not? It seems simple to me. Simple doesn't mean easy. Factoring a 2048 bit number is very simple and very hard.
- cma 11y agoBecause then anything that can be proven in a given axiom system is considered simple because it can be done by enumerating each possible sequence of transformations.
- dexterdog 11y agoIt might be easier to read the list of all discovered problems. Then everything else is in play.
- ColinWright 11y agoNot to answer your question, but here's a simple, unsolved problem: Dissect the circle into congruent pieces such that the center point is in the interior of one of the pieces. It is widely believed to be impossible, but neither proof of impossibility nor construction of an example have been found.
- aetherson 11y agoHuh. Is it possible to dissect a circle into congruent pieces that are not, uh, pie shapes? Is that the question, or are there known other ways to dissect a circle into congruent pieces, it's just those pieces also have the center point as an edge point?
- ColinWright 11y agoYes. Summarising, it is possible to dissect a circle into finitely many congruent pieces that do not all touch the center point. Slightly longer, there are at least two infinite families of solutions: (a) For every natural number n>1 there are f(n)>0 solutions, with f growing exponentially quickly. (b) For every natural number n>1 there is an uncountable infinite family. Thus we have a countable family of solutions, and a countable family of continuous solutions. So yes, there are solutions that are not all just "slicing a pizza" type solutions.
- jameshart 11y agoNon pie shapes are definitely possible - look at the taijitu (yin/yang) symbol for example - . But of course, again, the center is on the divide between both halves.
- robinhouston 11y agoThere's a nice collection on Math Overflow: Not especially famous, long-open problems which anyone can understand http://mathoverflow.net/q/100265/8217 http://mathoverflow.net/q/100265/8217