Remarks on perspective simplices
The planar figure of two triangles being in perspective position is associated with a theorem of Desargues, which is responsible for the fact that the coordinate set of the plane is a field. This well-known theorem of Desargues allows the obvious interpretation in space of a three-sided pyramid, whi...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University of Belgrade - Faculty of Mechanical Engineering, Belgrade
2017-01-01
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| Series: | FME Transactions |
| Subjects: | |
| Online Access: | https://scindeks-clanci.ceon.rs/data/pdf/1451-2092/2017/1451-20921702243W.pdf |
| _version_ | 1818146081139064832 |
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| author | Weiss Gunter Ebisui H. |
| author_facet | Weiss Gunter Ebisui H. |
| author_sort | Weiss Gunter |
| collection | DOAJ |
| description | The planar figure of two triangles being in perspective position is associated with a theorem of Desargues, which is responsible for the fact that the coordinate set of the plane is a field. This well-known theorem of Desargues allows the obvious interpretation in space of a three-sided pyramid, which is intersected by two planes. The article is dedicated to generalizing this theorem of Desargues to perspective simplices in a projective n-space and their linear images in a subspace. Hereby one can find remarkable incidences and configurations. Starting point to this investigation is a planar figure of perspective quadrangles, where the second author discovered a remarkable coincidence figure. The proof of this incidence statement is based on an interpretation of the planar 'Ebisui figure' as the central projection of a (projective) cross-polytope in 4-space. This principle can also be extended to higher dimensions. |
| first_indexed | 2024-12-11T12:13:41Z |
| format | Article |
| id | doaj.art-26f473a1cbb443d48928a7c8cf73c8ac |
| institution | Directory Open Access Journal |
| issn | 1451-2092 2406-128X |
| language | English |
| last_indexed | 2024-12-11T12:13:41Z |
| publishDate | 2017-01-01 |
| publisher | University of Belgrade - Faculty of Mechanical Engineering, Belgrade |
| record_format | Article |
| series | FME Transactions |
| spelling | doaj.art-26f473a1cbb443d48928a7c8cf73c8ac2022-12-22T01:07:43ZengUniversity of Belgrade - Faculty of Mechanical Engineering, BelgradeFME Transactions1451-20922406-128X2017-01-014522432501451-20921702243WRemarks on perspective simplicesWeiss Gunter0Ebisui H.1Universities of Technology, Dresden and Vienna Institute for Geometry, AustriaOval Research Centre, Iwakuni, JapanThe planar figure of two triangles being in perspective position is associated with a theorem of Desargues, which is responsible for the fact that the coordinate set of the plane is a field. This well-known theorem of Desargues allows the obvious interpretation in space of a three-sided pyramid, which is intersected by two planes. The article is dedicated to generalizing this theorem of Desargues to perspective simplices in a projective n-space and their linear images in a subspace. Hereby one can find remarkable incidences and configurations. Starting point to this investigation is a planar figure of perspective quadrangles, where the second author discovered a remarkable coincidence figure. The proof of this incidence statement is based on an interpretation of the planar 'Ebisui figure' as the central projection of a (projective) cross-polytope in 4-space. This principle can also be extended to higher dimensions.https://scindeks-clanci.ceon.rs/data/pdf/1451-2092/2017/1451-20921702243W.pdfprojective spaceharmonic homologydesargues' theoremsimplexcross polytopepolyhedron (msc 2000: 51a20, 51m05) |
| spellingShingle | Weiss Gunter Ebisui H. Remarks on perspective simplices FME Transactions projective space harmonic homology desargues' theorem simplex cross polytope polyhedron (msc 2000: 51a20, 51m05) |
| title | Remarks on perspective simplices |
| title_full | Remarks on perspective simplices |
| title_fullStr | Remarks on perspective simplices |
| title_full_unstemmed | Remarks on perspective simplices |
| title_short | Remarks on perspective simplices |
| title_sort | remarks on perspective simplices |
| topic | projective space harmonic homology desargues' theorem simplex cross polytope polyhedron (msc 2000: 51a20, 51m05) |
| url | https://scindeks-clanci.ceon.rs/data/pdf/1451-2092/2017/1451-20921702243W.pdf |
| work_keys_str_mv | AT weissgunter remarksonperspectivesimplices AT ebisuih remarksonperspectivesimplices |