An excursion in finite geometry

Tondini, Daniela

doi:10.1080/09720502.2020.1712843

Cited by 3 publications

(3 citation statements)

References 11 publications

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“…The reason for deciding to conduct a detailed investigation of this special case is the charm of small projective planes, cf. [1], [3], [5], [6], [9] and [10].…”

Section: Introductionmentioning

confidence: 99%

Discovering Doily in PG(2,5)

Innamorati¹

2023

Preprint

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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 two, GQ(2,2), whose representation has been dubbed “the doily” by Stan Payne in 1973. In this paper 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 two.

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“…The reason for deciding to conduct a detailed investigation of this special case is the charm of small projective planes, cf. [1], [3], [5], [6], [9] and [10].…”

Section: Introductionmentioning

confidence: 99%

Discovering Doily in PG(2,5)

Innamorati¹

2023

Preprint

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“…The reason for deciding to conduct a detailed investigation of this special case is the charm of small projective planes, cf. [3][4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Note on Discovering Doily in PG(2,5)

Innamorati

2023

Mathematics

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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.

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“…We present the topic in a readable fashion, with particular attention to showing how original ideas of mathematics arise naturally from considerations well known to elementary students. Those with a good knowledge of school geometry should find the article very helpful as a bridge between old and new ideas, see also [12], [13], [18], [19] and [20],…”

Section: Introductionmentioning

confidence: 99%