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1. Problem of Apollonius: Problem
2. Problem of Apollonius: Euclidean
 
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1. Problem of Apollonius: Problem of Apollonius, Euclidean Geometry, Circle, Tangent, Apollonius of Perga, Pappus of Alexandria, Adriaan van Roomen, Hyperbola
Paperback: 156 Pages (2010-01-18)
list price: US$70.00
Isbn: 6130343302
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Editorial Review

Product Description
High Quality Content by WIKIPEDIA articles! In Euclidean plane geometry, Apollonius' problem is to construct circles that are tangent to three given circles in a plane. Apollonius of Perga posed and solved this famous problem in his work ??????; this work has been lost, but a 4th-century report of his results by Pappus of Alexandria has survived. Three given circles generically have eight different circles that are tangent to them and each solution circle encloses or excludes the three given circles in a different way.In the 16th century, Adriaan van Roomen solved the problem using intersecting hyperbolas, but this solution does not use only straightedge and compass constructions. François Viète found such a solution by exploiting limiting cases: any of the three given circles can be shrunk to zero radius or expanded to infinite radius. ... Read more


2. Problem of Apollonius: Euclidean Geometry, Circle, Tangent, Apollonius of Perga, Pappus of Alexandria, Adriaan van Roomen, Hyperbola, Compass and Straightedge Constructions, Franciscus Vieta
Paperback: 128 Pages (2010-01-26)
list price: US$64.00
Isbn: 6130348207
Canada | United Kingdom | Germany | France | Japan
Editorial Review

Product Description
High Quality Content by WIKIPEDIA articles! n Euclidean plane geometry, Apollonius' problem is to construct circles that are tangent to three given circles in a plane. Apollonius of Perga (ca. 262 BC ? ca. 190 BC) posed and solved this famous problem in his work ?????? (Epaphaí, "Tangencies"); this work has been lost, but a 4th-century report of his results by Pappus of Alexandria has survived. Three given circles generically have eight different circles that are tangent to them (Figure 2) and each solution circle encloses or excludes the three given circles in a different way. ... Read more


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