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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.
10
votes
Accepted
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, …