Zobrazeno 1 - 10
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pro vyhledávání: '"Inscribed square problem"'
Akademický článek
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Autor:
Richard Evan Schwartz
Publikováno v:
Advances in Geometry.
We prove an integral formula for continuous paths of rectangles inscribed in a piecewise smooth loop. We use this integral formula to prove the inequality M(γ) ≥ Δ(γ)/2 – 1, where M(γ) denotes the total multiplicity of rectangle coincidences,
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::6a8748a35c5fe9f76d645380d018ff7a
https://doi.org/10.1515/advgeom-2021-0012
https://doi.org/10.1515/advgeom-2021-0012
Publikováno v:
Forum of Mathematics, Sigma. 8
Toeplitz conjectured that any simple planar loop inscribes a square. Here we prove variants of Toeplitz' square peg problem. We prove Hadwiger's 1971 conjecture that any simple loop in $3$-space inscribes a parallelogram. We show that any simple plan
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7b0e285dceee683d5af53b10a3c27da1
https://doi.org/10.1017/fms.2019.51
https://doi.org/10.1017/fms.2019.51
Akademický článek
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Publikováno v:
Discrete & Computational Geometry. 51:722-728
In 1911, Toeplitz made a conjecture asserting that every Jordan curve in \(\mathbb{R}^{2}\) contains four points forming the corners of a square. Here Conjecture C is presented, which states that the side length of the largest square on a closed curv
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::fa5f76e557c725ad8119443a3948823a
https://doi.org/10.1007/s00454-014-9578-5
https://doi.org/10.1007/s00454-014-9578-5
Autor:
Terence Tao
The "square peg problem" or "inscribed square problem" of Toeplitz asks if every simple closed curve in the plane inscribes a (non-degenerate) square, in the sense that all four vertices of that square lie on the curve. By a variety of arguments of a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f1f77b4c6a36790874b81c0a8a745b22
Publikováno v:
Journal of Discrete Algorithms. 13:78-85
We consider approximation algorithms for the problem of computing an inscribed rectangle having largest area in a convex polygon on n vertices. If the order of the vertices of the polygon is given, we present a randomized algorithm that computes an i
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::631115f4727e40c414eea4239983acad
https://doi.org/10.1016/j.jda.2012.01.002
https://doi.org/10.1016/j.jda.2012.01.002
Autor:
Senlin Wu, Horst Martini
Publikováno v:
Colloquium Mathematicum. 120:249-261
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::3fd70e8d6065262b953929784306f70c
https://doi.org/10.4064/cm120-2-5
https://doi.org/10.4064/cm120-2-5
Autor:
V. Makeev
Publikováno v:
St. Petersburg Mathematical Journal. 16:815-820
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::e6419cfba2e4fd58c13647395e87f7d2
https://doi.org/10.1090/s1061-0022-05-00880-0
https://doi.org/10.1090/s1061-0022-05-00880-0
Autor:
Benjamin Matschke
Publikováno v:
Notices of the American Mathematical Society
This is a short survey article on the 102 years old Square Peg Problem of Toeplitz, which is also called the Inscribed Square Problem. It asks whether every continuous simple closed curve in the plane contains the four vertices of a square. This arti
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::21418ea916d90a18f33d1d4e8ac97f3c
https://hdl.handle.net/21.11116/0000-0004-15B8-521.11116/0000-0004-15BA-3
https://hdl.handle.net/21.11116/0000-0004-15B8-521.11116/0000-0004-15BA-3