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5:22 AM
I suppose that on questions tagged geometry+euclidean-geometry, the deprecated tag can be replaced by . There are only 5 questions that do not already have the mg.metric-geometry tag.
Q: Point cloud that maximizes the minimum pairwise distance in Euclidean space

gondolierI am interested finding the collection of points in the Euclidean space that has the maximal minimal pairwise distance subject to an average norm constraint, that is, how to maximize $min_{i \neq j} |x_i - x_j|$ subject to $\frac{1}{n} \sum_{i=1}^n |x_j|^2 \leq1$ where $\{x_1, \ldots, x_n\} \su...

Q: Decomposing the plane into intervals

Ross MillikanI posted this on Stack Exchange and got a lot of interest, but no answer. A recent Missouri State problem stated that it is easy to decompose the plane into half-open intervals and asked us to do so with intervals pointing in every direction. That got me trying to decompose the plane into closed...

Q: Can we alter the axioms of Euclidean space to have $\mathbb{Q}^3$ as a unique model?

Hans-Peter StrickerI posted this question at math.stackexchange.com but didn't get an answer. Motivation Physicists are in search for a model of discrete space(-time) for a long time. So I wondered why not start with a "somehow discrete" space? How far do we get? Question Can we alter the axioms of Euclidean s...

Q: Action of Isometries on a Line in the Plane

MiamiMathI'm trying to determine the stabilizer of a line in a plane when acted upon by the group of isometries of the plane. Please note that I'm using the notation found in the Wikipedia article on Euclidean plane isometries. I've identified (and hopefully exhausted) the following isometries that will ...

Q: Worst-case nearest-neighbor distances between regions

Denis MatijevicSuppose that $S_1,\dots,S_n$ is a collection of disjoint shapes in the plane, and let $\mathcal{X}$ denote the set of all $n$-tuples of points $\lbrace x_1,\dots,x_n\rbrace$ such that $x_i\in S_i$ for each $i$. For any such tuple $X = \lbrace x_1,\dots,x_n\rbrace$, let $F(X)$ be defined as $F(X...


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