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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.
13
votes
The Ramanujan Problems
Concerning the planimetry problem: Having a suitable background, it is not hard to produce many puzzles like this. For example, here is one more pair of points on that mysterious circle: intersect a c …
6
votes
Determine if circle is covered by some set of other circles
The problem (for discs of arbitrary radii) is essentially equivalent to the following: given a convex polyhedral set in $\mathbb R^3$ (represented by a system of linear inequalities), determine whethe …
2
votes
Worst-case nearest-neighbor distances between regions
I assume you are seeking a lower bound for $r$ for configurations of a fixed total area $A$, otherwise it just does not make sense.
Yes the bound is $\sim C\sqrt{A/n}$ for some constant $C>0$ but I d …