1. bookVolume 25 (2017): Issue 2 (July 2017)
Journal Details
License
Format
Journal
eISSN
1898-9934
ISSN
1426-2630
First Published
09 Jun 2008
Publication timeframe
4 times per year
Languages
English
access type Open Access

Pascal’s Theorem in Real Projective Plane

Published Online: 23 Sep 2017
Volume & Issue: Volume 25 (2017) - Issue 2 (July 2017)
Page range: 107 - 119
Received: 27 Jun 2017
Journal Details
License
Format
Journal
eISSN
1898-9934
ISSN
1426-2630
First Published
09 Jun 2008
Publication timeframe
4 times per year
Languages
English
Summary

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]).

Keywords

MSC 2010

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