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Huh. 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 c
by aetherson 11y ago
Huh. 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.