Constructible circles on the unit sphere
In this paper we show how to give an intrinsic definition of a constructible circle on the sphere. The classical definition of constructible circle in the plane, using straight edge and compass is there by translated in ters of so called Lenart tools. The process by which we achieve our goal involve...
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ndltd-csusb.edu-oai-scholarworks.lib.csusb.edu-etd-project-26752019-10-23T03:31:05Z Constructible circles on the unit sphere Pauley, Blaga Slavcheva In this paper we show how to give an intrinsic definition of a constructible circle on the sphere. The classical definition of constructible circle in the plane, using straight edge and compass is there by translated in ters of so called Lenart tools. The process by which we achieve our goal involves concepts from the algebra of Hermitian matrices, complex variables, and Sterographic projection. However, the discussion is entirely elementary throughout and hopefully can serve as a guide for teachers in advanced geometry. 2000-01-01T08:00:00Z text application/pdf https://scholarworks.lib.csusb.edu/etd-project/1675 https://scholarworks.lib.csusb.edu/cgi/viewcontent.cgi?article=2675&context=etd-project Theses Digitization Project CSUSB ScholarWorks Analytic Geometry Geometry Constructibility (Set theory) Geometrical construction Hermitian structures Matrices Functions of complex variables Geometry and Topology |
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NDLTD |
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Others
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NDLTD |
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Analytic Geometry Geometry Constructibility (Set theory) Geometrical construction Hermitian structures Matrices Functions of complex variables Geometry and Topology |
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Analytic Geometry Geometry Constructibility (Set theory) Geometrical construction Hermitian structures Matrices Functions of complex variables Geometry and Topology Pauley, Blaga Slavcheva Constructible circles on the unit sphere |
| description |
In this paper we show how to give an intrinsic definition of a constructible circle on the sphere. The classical definition of constructible circle in the plane, using straight edge and compass is there by translated in ters of so called Lenart tools. The process by which we achieve our goal involves concepts from the algebra of Hermitian matrices, complex variables, and Sterographic projection. However, the discussion is entirely elementary throughout and hopefully can serve as a guide for teachers in advanced geometry. |
| author |
Pauley, Blaga Slavcheva |
| author_facet |
Pauley, Blaga Slavcheva |
| author_sort |
Pauley, Blaga Slavcheva |
| title |
Constructible circles on the unit sphere |
| title_short |
Constructible circles on the unit sphere |
| title_full |
Constructible circles on the unit sphere |
| title_fullStr |
Constructible circles on the unit sphere |
| title_full_unstemmed |
Constructible circles on the unit sphere |
| title_sort |
constructible circles on the unit sphere |
| publisher |
CSUSB ScholarWorks |
| publishDate |
2000 |
| url |
https://scholarworks.lib.csusb.edu/etd-project/1675 https://scholarworks.lib.csusb.edu/cgi/viewcontent.cgi?article=2675&context=etd-project |
| work_keys_str_mv |
AT pauleyblagaslavcheva constructiblecirclesontheunitsphere |
| _version_ |
1719275067885486080 |