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Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions (theorems) from these.

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Decomposing the plane into intervals

Conway and Croft show it can be done for closed intervals and cannot be done for open intervals in the paper: Covering a sphere with congruent great-circle arcs. Proc. Cambridge Philos. Soc. 60, 1964, …
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