scholarly journals The Regge symmetry, confocal conics, and the Schläfli formula

2019 ◽  
Vol 51 (5) ◽  
pp. 765-775
Author(s):  
Arseniy Akopyan ◽  
Ivan Izmestiev
Keyword(s):  
Schläfli Formula ◽  
Confocal Conics

2. Note on a Geometrical Theorem

1878 ◽  
Vol 9 ◽  
pp. 533-536
Author(s):  
Tait
Keyword(s):  
The Other ◽  
Geometrical Proof ◽  
In Trans ◽  
The Mean ◽  
Concentric Circles ◽  
Confocal Conics

In “Trans. R.S.E.” (1864–5) Fox Talbot proved very simply, by means of a species of co-ordinates depending on confocal conics, the following theorem, at the same time asking for a simple geometrical proof.If two sets of three concentric circles, with the same common difference of radii, intersect one another—the chords of the arcs intercepted on the mean circle of each series by the extremes of the other are equal.

1. On Confocal Conics

1866 ◽  
Vol 5 ◽  
pp. 432-432
Author(s):  
H. Fox Talbot
Keyword(s):  
Confocal Conics

scholarly journals A contribution to the confocal conics

1880 ◽  
Vol 009 (3) ◽  
pp. 109-112
Author(s):  
Václav Jeřábek
Keyword(s):  
Confocal Conics

scholarly journals Trigonometric identities and volumes of the hyperbolic twist knot cone-manifolds

2014 ◽  
Vol 23 (12) ◽  
pp. 1450064 ◽  
Author(s):  
Ji-Young Ham ◽  
Alexander Mednykh ◽  
Vladimir Petrov
Keyword(s):  
Singular Locus ◽  
Schläfli Formula ◽  
Cyclic Coverings ◽  
Trigonometric Identities

We calculate the volumes of the hyperbolic twist knot cone-manifolds using the Schläfli formula. Even though general ideas for calculating the volumes of cone-manifolds are around, since there is no concrete calculation written, we present here the concrete calculations. We express the length of the singular locus in terms of the distance between the two axes fixed by two generators. In this way the calculation becomes easier than using the singular locus directly. The volumes of the hyperbolic twist knot cone-manifolds simpler than Stevedore's knot are known. As an application, we give the volumes of the cyclic coverings over the hyperbolic twist knots.

Confocal Conics in Space-Time

1962 ◽  
Vol 69 (1) ◽  
pp. 1 ◽  
Author(s):  
Garrett Birkhoff ◽  
Robert Morris
Keyword(s):  
Space Time ◽  
Confocal Conics
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