Zobrazeno 1 - 10
of 141
pro vyhledávání: '"Seven circles theorem"'
Publikováno v:
The Mathematical Intelligencer
The Mathematical Intelligencer, 2020, 42 (2), pp.61-65. ⟨10.1007/s00283-019-09952-1⟩
Mathematical Intelligencer
Mathematical Intelligencer, Springer Verlag, 2020, 42 (2), pp.61-65. ⟨10.1007/s00283-019-09952-1⟩
The Mathematical Intelligencer, 2020, 42 (2), pp.61-65. ⟨10.1007/s00283-019-09952-1⟩
Mathematical Intelligencer
Mathematical Intelligencer, Springer Verlag, 2020, 42 (2), pp.61-65. ⟨10.1007/s00283-019-09952-1⟩
In this note, we will explain the connection between the Seven Circles Theorem and hyperbolic geometry, then prove a stronger result about hyperbolic geometry hexagons which implies the Seven Circles Theorem as a special case.
Comment: 5 figures
Comment: 5 figures
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c145872fc93b1148505cbcbcd7938606
https://doi.org/10.1007/s00283-019-09952-1
https://doi.org/10.1007/s00283-019-09952-1
Autor:
John R. Silvester
Publikováno v:
The Mathematical Gazette. 102:280-301
The circles C1, & , Cn form a chain of length n if Ci touches Ci + 1, for i = 1, & , n − 1, and the chain is closed if also Cn touches C1. A cyclic chain is a chain for which all the circles touch another circle S, the base circle of the chain. If
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::5f562030bd08e3bf2a06fb18d26820c2
https://doi.org/10.1017/mag.2018.59
https://doi.org/10.1017/mag.2018.59
Autor:
Lienhard Wimmer
Publikováno v:
Discrete & Computational Geometry. 57:763-781
How has a sphere to be covered by n equal circles so that the angular radius of the circles will be as small as possible? In this note the problem is solved for $$n=8$$n=8 and the combinatorial type of the solution for $$n = 9$$n=9 is determined.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::01fb7ad72b4c94be6f45fd72d7a05325
https://doi.org/10.1007/s00454-017-9891-x
https://doi.org/10.1007/s00454-017-9891-x
Publikováno v:
Involve 10, no. 2 (2017), 345-360
We define an abstract Apollonian supergasket using the solution set of a certain Diophantine equation, showing that the solutions are in bijective correspondence with the circles of any concrete supergasket. Properties of the solution set translate d
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::83bd2a041bec00813f040e2bd394189e
https://doi.org/10.2140/involve.2017.10.345
https://doi.org/10.2140/involve.2017.10.345
Autor:
Günhan Caglayan
Publikováno v:
The Mathematics Teacher. 110:92-97
Steiner chain is defined as the sequence of n circles that are all tangent to two given nonintersecting circles. A closed chain, in particular, is one in which every circle in the sequence is tangent to the previous and next circles of the chain. In
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::aab6ad71641aac4c4bbe06157a479b11
https://doi.org/10.5951/mathteacher.110.2.0092
https://doi.org/10.5951/mathteacher.110.2.0092
Autor:
Katsuhiro Shiohama, Minoru Tanaka
Publikováno v:
Progress in Differential Geometry, K. Shiohama, ed. (Tokyo: Mathematical Society of Japan, 1993)
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b87cb31076483b48f772d7dada8eadf7
https://doi.org/10.2969/aspm/02210299
https://doi.org/10.2969/aspm/02210299
Autor:
Toshiaki Adachi
Publikováno v:
Topology and its Applications. 196:311-324
We show that every circle on a complex hyperbolic space except unbounded circles of complex torsion ±1 which have two distinct points at infinity can be regarded as a trajectory for some Sasakian magnetic field on some totally η -umbilic real hyper
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a903cb7c0f94e2c8c46e4bab49cb4f24
https://doi.org/10.1016/j.topol.2015.05.008
https://doi.org/10.1016/j.topol.2015.05.008
Autor:
Klara Stokes, Milagros Izquierdo
Publikováno v:
Ars mathematica contemporanea
We construct isometric point-circle configurations on surfaces from uniform maps. This gives one geometric realisation in terms of points and circles of the Desargues configuration in the real projective plane, and three distinct geometric realisatio
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b970f2cef36fe98f39969d99d795c1c6
https://doi.org/10.26493/1855-3974.787.925
https://doi.org/10.26493/1855-3974.787.925
Autor:
M. C. Fernández-Cabo
Publikováno v:
Journal of Architectural Engineering. 23
The present study analyzes how to trace a circle packing using a variable compass. Several of these circle packings have been used by artisans and designers to make ornamental patterns in a...
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::2a6582219d8c2703c2a11155b85144f0
https://doi.org/10.1061/(asce)ae.1943-5568.0000233
https://doi.org/10.1061/(asce)ae.1943-5568.0000233
Autor:
Bahman Kalantari, Jong Youll Park
Publikováno v:
Honam Mathematical Journal. 36:787-794
We prove three convex hull theorems on triangles andcircles. Given a triangle △and a point p, let △ ′ be the triangle eachof whose vertices is the intersection of the orthogonal line from ptoan extended edge of △. Let △ ′′ be the triang
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f48d23eeadd6a82dae1bf55e2711f8e9
https://doi.org/10.5831/hmj.2014.36.4.787
https://doi.org/10.5831/hmj.2014.36.4.787