Geometrijska mjesta točaka

Laštro, Ivana (2014) Geometrijska mjesta točaka. Diploma thesis, Faculty of Science > Department of Mathematics.

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Abstract

In this work we analyze the geometric loci of points. The work is divided into five chapters. In the first chapter we are introduced to the definition of the locus of points and basic theorems related to loci of points. Also, in the first chapter, we meet one of the ways of determining the geometric places, which is the use of an empirical approach that requires geometric view. We give a few examples showing how to determine and accurately prove that a certain set is the required geometric place of the points that meet certain conditions. In the second chapter we meet with one of the constructive methods whereby the requested object is constructed as the intersection of some loci of points. In this section, we provide loci for some simple, widely known situations and apply that to the more complex structures. In the third section of this work we describe how a dynamic geometry program helps us in determining the locus of points when the geometric condition is too complicated for freehand drawing. Specifically, this chapter explains how to find geometric places of points using Sketchpad. The fourth chapter deals with the analytical finding of geometric loci and shows a few examples of how we can determine the geometric place of points using coordinates. The fifth chapter describes some famous curves that are defined as loci of points, such as the conic sections (ellipse, hyperbola and parabola), the lemniscate and the Witch of Agnesi.

Item Type: Thesis (Diploma thesis)
Supervisor: Starčević, Maja
Date: 2014
Number of Pages: 67
Subjects: NATURAL SCIENCES > Mathematics
Divisions: Faculty of Science > Department of Mathematics
Depositing User: Iva Prah
Date Deposited: 03 Jun 2015 12:19
Last Modified: 03 Jun 2015 12:19
URI: http://digre.pmf.unizg.hr/id/eprint/3995

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