Zobrazeno 1 - 10 of 19 pro vyhledávání: '"John R. Silvester"'
1
On cardioids and Morley's theorem
Autor: John R. Silvester
Publikováno v: The Mathematical Gazette. 105:40-51
Morley’s trisector theorem says that the three intersections of the trisectors of the angles of a triangle, lying near the three sides respectively, form an equilateral triangle. See Figure 1. Morley discovered his theorem in 1899, and news of it q
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::76dbf5d6c43aa5b3eb967408f0ae6c41
https://doi.org/10.1017/mag.2021.6
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4
On touching circles
Autor: John R. Silvester
Publikováno v: The Mathematical Gazette. 102:460-470
The circles C1, … , Cn form a chain of length n, or an n-chain, if Ci touches Ci + 1, for i = 1, … , n − 1, and the chain is closed if also Cn touches C1. If Ci touches Ci + 1 at Qi, for i = 1, … , n (subscripts being interpreted modulo n), t
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::921995e0baf49642fccaa80c689fc620
https://doi.org/10.1017/mag.2018.113
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5
The seven circles theorem revisited
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
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6
Variations on a Japanese Temple theorem
Autor: John R. Silvester
Publikováno v: The Mathematical Gazette. 102:38-49
The following Japanese Temple geometry theorem appears in Fukagawa and Rigby [1]:Thoerem 1: The products of the radii of the excircles on each pair of opposite sides of a circumscribed quadrilateral are equal.See Figure 1. A circumscribed quadrilater
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::199e00370dd46e626c93ec2f8d517007
https://doi.org/10.1017/mag.2018.6
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7
Extremal area ellipses of a convex quadrilateral
Autor: John R. Silvester
Publikováno v: The Mathematical Gazette. 101:11-26
In this paper we are going to generalise some standard results about the ellipses of least or greatest area, respectively circumscribing or inscribed in a triangle, to the corresponding ellipses for a convex quadrilateral.Given ΔABC let D, E, F be t
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::9c7e31ec3e4ad272ed8af431e2716e17
https://doi.org/10.1017/mag.2017.2
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8
Droz-Farny constructions
Autor: John R. Silvester
Publikováno v: The Mathematical Gazette. 96:19-38
Notation: If A, B are points, then AB denotes the line AB rather than just the segment from A to B, unless stated otherwise. If l, m are lines, then their meet is denoted l m. The circle through points A, B and C (the circumcircle of ΔABC) is denote
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::57022c0dfc9e1aca39b9ce65680c4662
https://doi.org/10.1017/s0025557200003934
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10
Reflected circles, and congruent perspective triangles
Autor: John R. Silvester
Publikováno v: The Mathematical Gazette. 93:10-26
For any three points X, Y, Z, let ⊙XYZ denote the circle through X, Y, Z (the circumcircle of ∆XYZ) or, if X, Y, Z happen to be collinear, the line XYZ. (We shall often regard lines as special circles, circles of infinite radius.) This paper is a
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::c5d874fc70cc46cf3eddcb13d15d52de
https://doi.org/10.1017/s0025557200184141
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