Note on Discovering Doily in PG(2,5)
W. L. Edge proved that the internal points of a conic in PG(2,5), together with the collinear triples on the non-secant lines, form the Desargues configuration. M. Saniga showed an intimate connection between Desargues configurations and the generalized quadrangles of order 2, GQ(2,2), whose represe...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-05-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/9/2210 |
| _version_ | 1797602186714152960 |
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| author | Stefano Innamorati |
| author_facet | Stefano Innamorati |
| author_sort | Stefano Innamorati |
| collection | DOAJ |
| description | W. L. Edge proved that the internal points of a conic in PG(2,5), together with the collinear triples on the non-secant lines, form the Desargues configuration. M. Saniga showed an intimate connection between Desargues configurations and the generalized quadrangles of order 2, GQ(2,2), whose representation was dubbed “the doily” by Stan Payne in 1973. In this note, we prove that the external points of a conic in PG(2,5), together with the collinear and non-collinear triples on the non-tangent lines, form the generalized quadrangle of order 2. |
| first_indexed | 2024-03-11T04:12:28Z |
| format | Article |
| id | doaj.art-bd5c52dbb75944618de5200bf7fa778a |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T04:12:28Z |
| publishDate | 2023-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-bd5c52dbb75944618de5200bf7fa778a2023-11-17T23:21:26ZengMDPI AGMathematics2227-73902023-05-01119221010.3390/math11092210Note on Discovering Doily in PG(2,5)Stefano Innamorati0Department of Industrial and Information Engineering and Economics, University of L’Aquila, Piazzale Ernesto Pontieri, 1 (Monteluco di Roio), I-67100 L’Aquila, ItalyW. L. Edge proved that the internal points of a conic in PG(2,5), together with the collinear triples on the non-secant lines, form the Desargues configuration. M. Saniga showed an intimate connection between Desargues configurations and the generalized quadrangles of order 2, GQ(2,2), whose representation was dubbed “the doily” by Stan Payne in 1973. In this note, we prove that the external points of a conic in PG(2,5), together with the collinear and non-collinear triples on the non-tangent lines, form the generalized quadrangle of order 2.https://www.mdpi.com/2227-7390/11/9/2210Desargues configurationgeneralized quadrangle of order twoprojective plane of order five |
| spellingShingle | Stefano Innamorati Note on Discovering Doily in PG(2,5) Mathematics Desargues configuration generalized quadrangle of order two projective plane of order five |
| title | Note on Discovering Doily in PG(2,5) |
| title_full | Note on Discovering Doily in PG(2,5) |
| title_fullStr | Note on Discovering Doily in PG(2,5) |
| title_full_unstemmed | Note on Discovering Doily in PG(2,5) |
| title_short | Note on Discovering Doily in PG(2,5) |
| title_sort | note on discovering doily in pg 2 5 |
| topic | Desargues configuration generalized quadrangle of order two projective plane of order five |
| url | https://www.mdpi.com/2227-7390/11/9/2210 |
| work_keys_str_mv | AT stefanoinnamorati noteondiscoveringdoilyinpg25 |