Konstrukcije trokuta ako su zadanetri specifične točke trokuta

master's thesis

• Author: Marta Topić Mlakar
• Mentor: Sanja Varošanec (mentor)
• Committee member: Sanja Varošanec (predsjednik povjerenstva)
• Committee member: Mea Bombardelli (član povjerenstva)
• Committee member: Ivica Nakić (član povjerenstva)
• Committee member: Marcela Hanzer (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2014-09-24, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Matematičar William Wernick, objavio je 1982. godine, svoje rezultate proučavanja konstrukcija trokuta sa zadane tri specifične točke trokuta. Specifičnim točkama trokuta proglasio je njegova tri vrha, tri polovišta, tri nožišta visina, tri nožišta simetrala kutova, ortocentar, težište te središta opisane i upisane kružnice trokuta. Od tih šesnaest točaka, sastavio je listu sa sto trideset i devet konstruktivnih problema. Na početku ovog rada definiran je pojam euklidskih konstrukcija jer će rješivost konstruktivnih problema ovisiti o mogućnosti izvođenja konstrukcije ravnalom i šestarom. Dalje su definirane specifične točke trokuta i navedena neka njihova svojstva. Rad sadrži i rješenja više konstruktivnih problema s liste W. Wernicka. Četvrto je poglavlje posvećeno proširenju liste konstrukcija trokuta sa zadane tri specifične točke trokuta. Harold Connelly je izvornoj listi od šesnaest točaka dodao još četiri točke, tri Eulerove točke i središte kružnice devet točaka. Njihovo je dodavanje izvornim točkama dovelo do proširenja liste W. Wernicka i novih sto i četrdeset konstruktivnih problema. Neki od njih također su riješeni u radu.

Abstract (english)

n 1982, mathematician William Wernick published his results on studying triangle constructions with three located points. He defined triangle’s three vertices, three feet of the medians, three feet of the altitudes, three feet of the internal angle bisectors, circumcenter, centroid, orthocenter and incenter as the specific points of a triangle. He used these sixteen points and made a list of one hundred and thirty-nine constructive problems. The term of Euclidean construction is defined in the beginning of this thesis because the solvability of constructive problems depends on the possibility of constructing with ruler and compass. Specific points of a triangle and some of their characteristics have been defined further on. Thesis also includes the solutions of different constructive problems from W. Wernick’s list. The fourth chapter is an overview of an extended list of constructive problems with three located points. To the original list of sixteen points, Harold Connelly has added four extra points, three Euler points and the center of a nine-point circle. By adding these points, W. Wernick’s list has been extended with one hundred and forty new constructive problems. Solutions to some of these problems can also be found in this thesis.

• Keywords: specifične točke trokuta; William Wernick; konstrukcije ravnalom i šestarom; Harold Connelly
• Keywords (english): specific points of a triangle; William Wernick; constructing with ruler and compass; Harold Connelly
• Language: croatian
• URN:NBN: urn:nbn:hr:217:378338
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Access restricted to students and staff of home institution
• Created on: 2019-02-18 11:15:51