# Pascal’s Theorem in Real Projective Plane

Formalized Mathematics (2017)

• Volume: 25, Issue: 2, page 107-119
• ISSN: 1426-2630

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## Abstract

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In this article we check, with the Mizar system [2], Pascal’s theorem in the real projective plane (in projective geometry Pascal’s theorem is also known as the Hexagrammum Mysticum Theorem)1. Pappus’ theorem is a special case of a degenerate conic of two lines. For proving Pascal’s theorem, we use the techniques developed in the section “Projective Proofs of Pappus’ Theorem” in the chapter “Pappus’ Theorem: Nine proofs and three variations” [11]. We also follow some ideas from Harrison’s work. With HOL Light, he has the proof of Pascal’s theorem2. For a lemma, we use PROVER93 and OTT2MIZ by Josef Urban4 [12, 6, 7]. We note, that we don’t use Skolem/Herbrand functions (see “Skolemization” in [1]).

## How to cite

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Roland Coghetto. "Pascal’s Theorem in Real Projective Plane." Formalized Mathematics 25.2 (2017): 107-119. <http://eudml.org/doc/288381>.

@article{RolandCoghetto2017,
abstract = {In this article we check, with the Mizar system [2], Pascal’s theorem in the real projective plane (in projective geometry Pascal’s theorem is also known as the Hexagrammum Mysticum Theorem)1. Pappus’ theorem is a special case of a degenerate conic of two lines. For proving Pascal’s theorem, we use the techniques developed in the section “Projective Proofs of Pappus’ Theorem” in the chapter “Pappus’ Theorem: Nine proofs and three variations” [11]. We also follow some ideas from Harrison’s work. With HOL Light, he has the proof of Pascal’s theorem2. For a lemma, we use PROVER93 and OTT2MIZ by Josef Urban4 [12, 6, 7]. We note, that we don’t use Skolem/Herbrand functions (see “Skolemization” in [1]).},
author = {Roland Coghetto},
journal = {Formalized Mathematics},
keywords = {Pascal’s theorem; real projective plane; Grassman-Plücker relation},
language = {eng},
number = {2},
pages = {107-119},
title = {Pascal’s Theorem in Real Projective Plane},
url = {http://eudml.org/doc/288381},
volume = {25},
year = {2017},
}

TY - JOUR
AU - Roland Coghetto
TI - Pascal’s Theorem in Real Projective Plane
JO - Formalized Mathematics
PY - 2017
VL - 25
IS - 2
SP - 107
EP - 119
AB - In this article we check, with the Mizar system [2], Pascal’s theorem in the real projective plane (in projective geometry Pascal’s theorem is also known as the Hexagrammum Mysticum Theorem)1. Pappus’ theorem is a special case of a degenerate conic of two lines. For proving Pascal’s theorem, we use the techniques developed in the section “Projective Proofs of Pappus’ Theorem” in the chapter “Pappus’ Theorem: Nine proofs and three variations” [11]. We also follow some ideas from Harrison’s work. With HOL Light, he has the proof of Pascal’s theorem2. For a lemma, we use PROVER93 and OTT2MIZ by Josef Urban4 [12, 6, 7]. We note, that we don’t use Skolem/Herbrand functions (see “Skolemization” in [1]).
LA - eng
KW - Pascal’s theorem; real projective plane; Grassman-Plücker relation
UR - http://eudml.org/doc/288381
ER -

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