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Results tagged with euclidean-geometry
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user 172802
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.
3
votes
Accepted
Is the max-centre map continuous for open bounded domains?
The result is not necessarily true. Consider for $n\geq1$ the open ball $R_n$ with diameter from $(\frac{1}{n},0)$ to $(\frac{1}{n+1},0)$. Let $L_n$ be the reflection of $R_n$ with respect to the $y$ …
- 10.6k
2
votes
Accepted
Does this property characterize straight lines in the plane?
It seems $\gamma:\mathbb{R}\to\mathbb{R}^2$ (I assume $\gamma$ is injective and continuous) is indeed a line. My argument is very similar to the one by Ilkka Törmä (I thought I could write a shorter o …
- 10.6k
5
votes
Convergence of sequences formed by orthocenters, incenters, and centroids in repeated triang...
Below I give an example of a triangle which seems to grow exponentially when iterating the process from the question (so it satisfies Scenario 3). The example relies on the existence of a fixed point …
- 10.6k