Konstrukcije trokuta ako su zadane tri specifične točke trokuta

Topić Mlakar, Marta (2014) Konstrukcije trokuta ako su zadane tri specifične točke trokuta. Diploma thesis, Faculty of Science > Department of Mathematics.

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Abstract

In 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.

Item Type: Thesis (Diploma thesis)
Supervisor: Varošanec, Sanja
Date: 2014
Number of Pages: 46
Subjects: NATURAL SCIENCES > Mathematics
Divisions: Faculty of Science > Department of Mathematics
Depositing User: Iva Prah
Date Deposited: 14 Jul 2015 12:36
Last Modified: 14 Jul 2015 12:36
URI: http://digre.pmf.unizg.hr/id/eprint/4126

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