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of 583
pro vyhledávání: '"51M04"'
Two subsets $A, B$ of the plane are betweenness isomorphic if there is a bijection $f\colon A\to B$ such that, for every $x,y,z\in A$, the point $f(z)$ lies on the line segment connecting $f(x)$ and $f(y)$ if and only if $z$ lies on the line segment
Externí odkaz:
http://arxiv.org/abs/2412.02495
Autor:
Kanda, Shuho, Koizumi, Junnosuke
An iterated circumcenter sequence (ICS) in dimension $d$ is a sequence of points in $\mathbb{R}^d$ where each point is the circumcenter of the preceding $d+1$ points. The purpose of this paper is to completely determine the parameter space of ICSs an
Externí odkaz:
http://arxiv.org/abs/2407.19767
Autor:
Aliyev, Yagub N.
We study the dual of Philo's shortest line segment problem which asks to find the optimal line segments passing through two given points, with a common endpoint, and with the other endpoints on a given line. The provided solution uses multivariable c
Externí odkaz:
http://arxiv.org/abs/2406.05702
Autor:
Kong, Yong, Zhang, Shaowei
Publikováno v:
American Mathematical Monthly, 2016, 123(8): 814-816
In the "classical" adventitious angle problem, for a given set of three angles $a$, $b$, and $c$ measured in integral degrees in an isosceles triangle, a fourth angle $\theta$ (the derived angle), also measured in integral degrees, is sought. We gene
Externí odkaz:
http://arxiv.org/abs/2405.02352
Autor:
Mandelkern, Mark
Publikováno v:
Amer. Math. Monthly 131 (2024), 162-163
A long-standing, unanswered question regarding Euclid's Elements concerns the absence of a theorem for the concurrence of the altitudes of a triangle, and the possible reasons for this omission. In the centuries following Euclid, a remarkable number
Externí odkaz:
http://arxiv.org/abs/2403.19670
Autor:
Mandelkern, Mark
Publikováno v:
Acta Math. Hungar. 150 (2016), 121-130
The Sylvester-Gallai Theorem, stated as a problem by J. J. Sylvester in 1893, asserts that for any finite, noncollinear set of points on a plane, there exists a line passing through exactly two points of the set. First, it is shown that for the real
Externí odkaz:
http://arxiv.org/abs/2402.03662
Autor:
Ansari, Mohammad
Let $\Bbb D$ be the open unit disk in the complex plane. In this note, for the Carleson set $S(b,h)$ and the Carleson window $W(b,h)$ which are particular subsets of $\Bbb D$, we find conditions on $h$ under which we have $W(b,h/c)\subset S(b,h)\subs
Externí odkaz:
http://arxiv.org/abs/2401.14415
Autor:
Aliyev, Yagub N.
Publikováno v:
Elemente der Mathematik 2024
In the paper we prove generalization of Schl\"omilch's and Zetel's theorems about concurrent lines in a triangle. This generalization is obtained as a corollary of sharp geometric inequality about the ratio of triangular areas which is proved using d
Externí odkaz:
http://arxiv.org/abs/2401.00930
Autor:
Bakaev, Egor, Kozhevnikov, Pavel
Two triangles are called orthologic if the perpendiculars from the vertices of one of them to the sides of the other are concurrent. In this paper, we explore the concept of orthology from various points of view. Mostly we work in terms of elementary
Externí odkaz:
http://arxiv.org/abs/2312.13893
Autor:
Richeson, David
A residue design is an artistic geometric construction in which we have $n$ equally-spaced points on a circle numbered 0 through $n-1$ and we join with a line segment each point $k$ to $ak$ modulo $n$ for some fixed $a\ge 2.$ The envelopes of these l
Externí odkaz:
http://arxiv.org/abs/2311.15101