Does anyone know of a catalog of sorts for what shapes are allowed for tiling a circular disk? For example, if you are allowed one piece to tile the disk, are all the possibilities essentially "pie"-shaped wedges, like these examples below?
...where all the pieces meet at a common point at the center of the circle, and all the pieces have an edge which makes up the circumference of the disk? Are all one-piece tilings rotationally symmetric? Or are there other possibilities of exactly covering the disk with a single tile? What about for two or more different tiles? Is there a better set of terms I should use in my search?
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2$\begingroup$ This question (and especially the answers) might interest you. I think you'll find there are many open problems in this direction. $\endgroup$ – Dan Rust Jun 25 '15 at 22:57
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1$\begingroup$ A slightly related MathOverflow thread: Is it possible to dissect a disk into congruent pieces, so that a neighborhood of the origin is contained within a single piece? $\endgroup$ – Zev Chonoles Jun 25 '15 at 22:59
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$\begingroup$ Yes, those are definitely interesting, and certainly answer the question about whether each tile has to have an edge on the circumference. $\endgroup$ – Greg Buchholz Jun 25 '15 at 23:07
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I found one example of a tessellation that doesn't use sectors.
https://www.math.nmsu.edu/~breakingaway/Lessons/TOAC/TOAC.htm
Not sure if there are others, but that might give you ideas.
