Konstrukcije trikotnika s tremi znanimi točkami

magistrsko delo

Anja Kozinc (Author), Klemen Šivic (Mentor)

Abstract

Zanima nas, ali lahko s šestilom in ravnilom konstruiramo trikotnik $\triangle ABC$, če imamo v ravnini podane tri točke iz množice \{oglišča, razpolovišča stranic, nožišča višin, presečišča stranic s simetralami kotov, središči očrtane in včrtane krožnice, višinska točka, težišče\}. Omenjena množica nam ponuja $139$ netrivialnih in bistveno različnih možnih trojic točk, npr.\ trojica $\{A, B, C\}$ je trivialna, trojico dveh oglišč in težišča pa lahko zapišemo kot $\{A, B, G\}, \{B, C, G\}$ ali $\{A, C, G\}$, kar so simetrični oz.\ analogni konstrukcijski problemi. Izmed teh trojic je $74$ takih, ki omogočajo konstrukcijo trikotnika $\triangle ABC$, poteki konstrukcij so zapisani v magistrskem delu.

Keywords

konstrukcija trikotnika;oglišča;središče očrtane krožnice;razpolovišča stranic;težišče;nožišča višin;višinska točka;središče včrtane krožnice;presečišča simetral kotov z nasprotno stranico;

Data

Language:	Slovenian
Year of publishing:	2020
Typology:	2.09 - Master's Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[A. Kozinc]
UDC:	514
COBISS:	50383875
Views:	1434
Downloads:	164
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Triangle constructions with three located points
Secondary abstract:	We would like to construct a triangle $\triangle ABC$, if we know positions of three points from the set \{vertices, feet of the medians, feet of the altitudes, feet of the internal angle bisectors, circumcenter, incenter, orthocenter, centroid\}. Then we have $139$ problems, all non-trivial and significantly distinct. For example, the triple of points $\{A, B, C\}$ is trivial, the selection of the triple of points to be two vertices and the centroid of a triangle could be listed as $\{A, B, G\}, \{B, C, G\}$ or $\{A, C, G\}$, which are all analogous. Only $74$ of these problems are solvable and we present their constructions.
Secondary keywords:	triangle construction;vertices;circumcenter;feet of the medians;centroid;feet of the altitudes;orthocenter;feet of the internal angle bisectors;incenter;
Type (COBISS):	Master's thesis/paper
Study programme:	0
Embargo end date (OpenAIRE):	1970-01-01
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Pedagoška matematika
Pages:	IX, 121 str.
ID:	12245773