Thébaultovi trije problemi : delo diplomskega seminarja

Filipič, Aljaž (author), Vavpetič, Aleš (mentor)

Victor Thébault je v letih 1937 in 1938 zastavil tri geometrijske probleme, ki so postali znani kot Thébaultovi trije problemi. V delu vse tri natančno formuliramo in dokažemo. Prva dva dokažemo z elementarnimi sredstvi evklidske geometrije, tretji, najzahtevnejši problem – Sawayama–Thébaultov izrek – pa zahteva močnejša orodja: pri dokazu uporabimo homotetijo, potenco točke in inverzijo. Osrednjo vlogo igra Sawayamova lema, ki je ključ do dokaza.

• Language: Slovenian
• Keywords: Thébaultovi izreki, paralelogram, kvadrat, enakostranični triko- tnik, včrtana krožnica, očrtana krožnica, Sawayamova lema, kolinearnost
• Work type: Final seminar paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2026
• PID: 20.500.12556/RUL-188188
• UDC: 514
• COBISS.SI-ID: 292212739
• Publication date in RUL: 19.09.2026

Secondary language

• Language: English
• Title: Thébault’s three problems

Abstract

In 1937 and 1938 Victor Thébault posed three geometric problems that became known as Thébault’s three problems. We state and prove all three. The first two are proved using elementary tools of Euclidean geometry, while the third and most demanding one – the Sawayama–Thébault theorem – requires more: its proof uses homothety, the power of a point and inversion. The central tool is Sawayama’s lemma, which is the key to the proof.

• Keywords: Thébault’s theorems, parallelogram, square, equilateral triangle, incircle, circumcircle, Sawayama’s lemma, collinearity