Konstrukcije pravilnog sedmerokuta

Lepen, Nikola (2016) Konstrukcije pravilnog sedmerokuta. Diploma thesis, Faculty of Science > Department of Mathematics.

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Abstract

The geometrical construction of regular polygons is an important part of geometry. It is known how to elementary (only by means of a ruler and a pair of compasses) construct an equilateral triangle, a square, a regular pentagon, a regular hexagon, a regular octagon, and a regular decagon. The first one missing in this sequence is a regular heptagon. While studying the construction of a regular heptagon, Gauß has determined the class of regular polygons that can be constructed elementary. Unfortunately, a heptagon is not one of them. However, a regular heptagon can be constructed if we use methods which are not parts of elementary constructions. For example, it can be constructed by inserting a line or using intersections of conics. We describe different constructions of a regular heptagon, starting from the analysis due to Archimedes and his conditions. Medieval Arab mathematicians tried to improve the work of Archimedes. We describe their constructions based on the work of Archimedes, as well as some of their original analyses concerning the construction of a regular heptagon. Some algebraic constructions have also been looked at. The solutions of an equation associated to a regular heptagon can be constructed using conics, mostly using intersections of a parabola and a hyperbola. We analyze a few interesting constructions of this type as well.

Item Type: Thesis (Diploma thesis)
Supervisor: Ilišević, Dijana
Date: 2016
Number of Pages: 60
Subjects: NATURAL SCIENCES > Mathematics
Divisions: Faculty of Science > Department of Mathematics
Depositing User: Iva Prah
Date Deposited: 07 Apr 2016 11:18
Last Modified: 07 Apr 2016 11:18
URI: http://digre.pmf.unizg.hr/id/eprint/4674

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