Konfiguracija 95 točk in 95 premic, ki izhaja iz Pascalovega izreka in posplošitve na višje rede : delo diplomskega seminarja

Terglav, Gašper (author), Šivic, Klemen (mentor)

V delu predstavimo konfiguracijo točk in premic, ki temelji na Pascalovem šestkotniku, ki je včrtan v stožnico. Nekatere rezultate posplošimo tudi na 2n-kotnik, včrtan v stožnico, pri tem se Pascalova premica spremeni v krivuljo višjega reda. Obravnavamo tudi iste izreke v dualni projektivni ravnini ter posplošimo Pascalov izrek v višjo dimenzijo. Pri dokazovanju uporabljamo predvsem posledico Bezoutovega izreka in Desarguesov izrek.

• Language: Slovenian
• Keywords: stožnica, kubika, Pascalova premica, Steinerjeva točka, Plückerjeva premica, Kirkmanova točka, Cayleyjeva premica, Salmonova točka, Bezoutov izrek, Desarguesov izrek.
• Work type: Final seminar paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2022
• PID: 20.500.12556/RUL-138808
• UDC: 514.7
• COBISS.SI-ID: 118601475
• Publication date in RUL: 19.08.2022

Secondary language

• Language: English
• Title: Pascal's mystic hexagon and generalizations to curves of higher order

Abstract

In this work we describe the configuration of points and lines, called Pascal's mystic hexagon. We also generalize the hexagon into a 2n-gon, present dual statements and extend Pascal's theorem into a higher dimension. We prove the classical results using Desargues' theorem. For other proofs we mostly use a corollary of Bezout's theorem.

• Keywords: conic, cubic, Pascal line, Steiner point, Plücker line, Kirkman point, Cayley line, Salmon point, Bezout's theorem, Desargues' theorem