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- Special_cases_of_Apollonius_problem abstract "In Euclidean geometry, Apollonius' problem is to construct all the circles that are tangent to three given circles. Special cases of Apollonius' problem are those in which at least one of the given circles is a point or line, i.e., is a circle of zero or infinite radius. The nine types of such limiting cases of Apollonius' problem are to construct the circles tangent to: three points (denoted PPP, generally 1 solution) three lines (denoted LLL, generally 4 solutions) one line and two points (denoted LPP, generally 2 solutions) two lines and a point (denoted LLP, generally 2 solutions) one circle and two points (denoted CPP, generally 2 solutions) one circle, one line, and a point (denoted CLP, generally 4 solutions) two circles and a point (denoted CCP, generally 4 solutions) one circle and two lines (denoted CLL, generally 8 solutions) two circles and a line (denoted CCL, generally 8 solutions)In a different type of limiting case, the three given geometrical elements may have a special arrangement, such as constructing a circle tangent to two parallel lines and one circle.".
- Special_cases_of_Apollonius_problem wikiPageExternalLink books?id=DkVUAAAAcAAJ.
- Special_cases_of_Apollonius_problem wikiPageID "16429785".
- Special_cases_of_Apollonius_problem wikiPageLength "16074".
- Special_cases_of_Apollonius_problem wikiPageOutDegree "28".
- Special_cases_of_Apollonius_problem wikiPageRevisionID "705535521".
- Special_cases_of_Apollonius_problem wikiPageWikiLink Angle_trisection.
- Special_cases_of_Apollonius_problem wikiPageWikiLink Apollonius_of_Perga.
- Special_cases_of_Apollonius_problem wikiPageWikiLink Axiom.
- Special_cases_of_Apollonius_problem wikiPageWikiLink Benjamin_Alvord_(mathematician).
- Special_cases_of_Apollonius_problem wikiPageWikiLink Category:Euclidean_plane_geometry.
- Special_cases_of_Apollonius_problem wikiPageWikiLink Celtic_knot.
- Special_cases_of_Apollonius_problem wikiPageWikiLink Compass-and-straightedge_construction.
- Special_cases_of_Apollonius_problem wikiPageWikiLink Compass_(drawing_tool).
- Special_cases_of_Apollonius_problem wikiPageWikiLink Euclid.
- Special_cases_of_Apollonius_problem wikiPageWikiLink Euclidean_geometry.
- Special_cases_of_Apollonius_problem wikiPageWikiLink Geometric_mean.
- Special_cases_of_Apollonius_problem wikiPageWikiLink Google_Books.
- Special_cases_of_Apollonius_problem wikiPageWikiLink Gothic_architecture.
- Special_cases_of_Apollonius_problem wikiPageWikiLink Heptagon.
- Special_cases_of_Apollonius_problem wikiPageWikiLink Hexagon.
- Special_cases_of_Apollonius_problem wikiPageWikiLink Inversive_geometry.
- Special_cases_of_Apollonius_problem wikiPageWikiLink Isosceles_triangle.
- Special_cases_of_Apollonius_problem wikiPageWikiLink Limiting_case_(mathematics).
- Special_cases_of_Apollonius_problem wikiPageWikiLink Mathematics.
- Special_cases_of_Apollonius_problem wikiPageWikiLink Pentagon.
- Special_cases_of_Apollonius_problem wikiPageWikiLink Polygon.
- Special_cases_of_Apollonius_problem wikiPageWikiLink Problem_of_Apollonius.
- Special_cases_of_Apollonius_problem wikiPageWikiLink Radical_axis.
- Special_cases_of_Apollonius_problem wikiPageWikiLink Symmetry.
- Special_cases_of_Apollonius_problem wikiPageWikiLinkText "Special cases of Apollonius' problem".
- Special_cases_of_Apollonius_problem wikiPageWikiLinkText "limiting case".
- Special_cases_of_Apollonius_problem wikiPageWikiLinkText "special cases of Apollonius' problem".
- Special_cases_of_Apollonius_problem wikiPageUsesTemplate Template:Cite_book.
- Special_cases_of_Apollonius_problem wikiPageUsesTemplate Template:Cite_journal.
- Special_cases_of_Apollonius_problem wikiPageUsesTemplate Template:Clarify.
- Special_cases_of_Apollonius_problem wikiPageUsesTemplate Template:Missing_information.
- Special_cases_of_Apollonius_problem subject Category:Euclidean_plane_geometry.
- Special_cases_of_Apollonius_problem hypernym Tangent.
- Special_cases_of_Apollonius_problem comment "In Euclidean geometry, Apollonius' problem is to construct all the circles that are tangent to three given circles. Special cases of Apollonius' problem are those in which at least one of the given circles is a point or line, i.e., is a circle of zero or infinite radius.".
- Special_cases_of_Apollonius_problem label "Special cases of Apollonius' problem".
- Special_cases_of_Apollonius_problem sameAs Q7574796.
- Special_cases_of_Apollonius_problem sameAs Casos_especials_del_problema_dApolxc2xb7loni.
- Special_cases_of_Apollonius_problem sameAs Q7574796.
- Special_cases_of_Apollonius_problem wasDerivedFrom Special_cases_of_Apollonius_problem?oldid=705535521.
- Special_cases_of_Apollonius_problem isPrimaryTopicOf Special_cases_of_Apollonius_problem.