Nejednakosti između osnovnih sredina

Nemec, Marko (2015) Nejednakosti između osnovnih sredina. Diploma thesis, Faculty of Science > Department of Mathematics.

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Abstract

Proving inequalities is an important part of mathematics. It is also an example of problems that are frequently given on mathematics competitions. In this thesis we have worked on inequalities between arithmetic, geometric, harmonic and quadratic means. The most famous inequality is the one between arithmetic and geometric mean. We have given four different proofs of that inequality. Beside of that, we have shown on a few examples how to use that inequality for proving other inequalities, and also for solving some other problems like finding maximum values of functions. Also, we have solved two problems from International Mathematical Olympiad, which are good examples of using inequality between arithmetic and geometric mean. In the remaining part of thesis, one can find proofs of inequalities between geometric and harmonic, and arithmetic and quadratic inequality, and also a few examples of the application of those inequalities.

Item Type: Thesis (Diploma thesis)
Supervisor: Bombardelli, Mea
Date: 2015
Number of Pages: 40
Subjects: NATURAL SCIENCES > Mathematics
Divisions: Faculty of Science > Department of Mathematics
Depositing User: Iva Prah
Date Deposited: 23 Oct 2015 10:03
Last Modified: 23 Oct 2015 10:03
URI: http://digre.pmf.unizg.hr/id/eprint/4174

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