Apollonian Cubics: An Application of Group Theory to a Problem in Euclidean Geometry

Pamfilos, Paris; Thoma, Apostolos

doi:10.2307/2690791

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Distinguishability Of Convex Polygons1

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2012

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“…Thus, I + is the bounded component of A + , I 0 is the unbounded component of A + , the points A 1 and B 1 are on I 0 , and the points A 2 and B 2 are on I + . Further, by [12,Proposition 7.1], the so-called middle line m separates I + and I 0 , that is, the components I + and I 0 are on different sides of m . Hence the configuration is much like the one seen on Figure 2.…”

Section: Distinguishability Of Convex Polygonsmentioning

confidence: 99%

“…If an Apollonian curve is reducible, then (a) it consists of a nondegenerate circle and a straight line through its centre, or (b) it consists of a degenerate circle and a straight line, or (c) it consists of a nondegenerate equilateral hyperbola and the line at infinity, or (d) it consists of two perpendicular straight lines and the line at infinity. Theorem 2.3 is clearly stated in[11, p. 358, l. -7] without proof, but there is a transparent proof of it in[12, Section 6] and a more detailed proof in[9, Section 2].…”

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confidence: 99%

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