On cyclic quadrilaterals in euclidean and hyperbolic geometries
On cyclic quadrilaterals in euclidean and hyperbolic geometries
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欧氏几何和双曲几何中的循环四边形
DOI：
10.5486/pmd.2021.8894
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发表时间：
2019-08
期刊：
影响因子：
--
通讯作者：
Xiaohui Zhang
中科院分区：
文献类型：
--
作者：
Gendi Wang;Matti Vuorinen;Xiaohui Zhang
Four points ordered in the positive order on the unit circle determine the vertices of a quadrilateral, which is considered either as a euclidean or as a hyperbolic quadrilateral depending on whether the lines connecting the vertices are euclidean or hyperbolic lines. In the case of hyperbolic lines, this type of quadrilaterals are called ideal quadrilaterals. Our main result gives a euclidean counterpart of an earlier result on the hyperbolic distances between the opposite sides of ideal quadrilaterals. The proof is based on computations involving hyperbolic geometry. We also found a new formula for the hyperbolic midpoint of a hyperbolic geodesic segment in the unit disk. As an application of some geometric properties, we provided a euclidean construction of the symmetrization of random four points on the unit circle with respect to a diameter which preserves the absolute cross ratio of quadruples.
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DOI：
10.1007/s40840-016-0439-7
发表时间：
2014-03
影响因子：
1.2
作者：
Gendi Wang
通讯作者：
Gendi Wang
DOI：
10.1080/00029890.2001.11919719
发表时间：
2001-01
期刊：
The American Mathematical Monthly
影响因子：
--
作者：
C. Goodman-Strauss
通讯作者：
C. Goodman-Strauss
DOI：
10.1142/9789812703279
发表时间：
2005
期刊：
--
影响因子：
--
作者：
A. Ungar
通讯作者：
A. Ungar
DOI：
10.1080/00029890.2008.11920506
发表时间：
2008-02
期刊：
The American Mathematical Monthly
影响因子：
--
作者：
A. Ungar
通讯作者：
A. Ungar
DOI：
10.1073/pnas.12.6.389
发表时间：
1926-06
影响因子：
11.1
作者：
J. Thomas
通讯作者：
J. Thomas