Primitivne pitagorejske trojke Gaussovih celih števil

diplomsko delo

Patricija Redenšek (Author), Daniel Eremita (Mentor)

Abstract

Pitagorejska trojka (x, y, z) je urejena trojka takih celih števil x, y in z, da velja x^2 + y^2 = z^2. Namen diplomskega dela je predstaviti metodo, s katero lahko generiramo vse rešitve enačbe alfa^2 + beta^2 = gama^2 v množici Gaussovih celih števil. Prvo poglavje je namenjeno predstavitvi značilnosti grške matematike in Pitagorovemu izreku. V drugem poglavju so podrobno predstavljena Gaussova cela števila in njihove lastnosti. Tretje poglavje je namenjeno obravnavi pitagorejskih trojk. Prvi del tega poglavja obravnava pitagorejske trojke celih števil. Temu sledi glavni del diplomskega dela, v katerem vpeljemo pojem primitivne pitagorejske trojke Gaussovih celih števil in proučimo lastnosti takih trojk.

Keywords

matematika;pitagorejska trojka;diofantska enačba;cela števila;Gaussova cela števila;diplomska dela;

Data

Language:	Slovenian
Year of publishing:	2009
Source:	Maribor
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[P. Redenšek]
UDC:	51(043.2)
COBISS:	17335304
Views:	3343
Downloads:	179
Average score:	0 (0 votes)
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Other data

Secondary language:	English
Secondary title:	PRIMITIVE PHYTHAGOREAN TRIPLES OF GAUSSIAN INTEGERS
Secondary abstract:	A Pythagorean triple (x ,y ,z) consists of three integers x, y and z, such that x^2 + y^2 = z^2. The purpose of this thesis is to present the method for generating all solution of the equation alpha^2 + beta^2 = gamma^2 in the set of Gaussian integers. First chapter represents features of Greek mathematics and the Pythagorean theorem. In the second chapter we have Gaussian integers and their characteristics. Third chapter represents Pythagorean triples. After that follows the main part of this thesis in which we introduce primitive Pythagorean triples of Gaussian integers and review their characteristics.
Secondary keywords:	Pythagorean triples;prime Pythagorean triples;Diophantine equation;integers;Gaussian integers;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	X, 63 f.
Keywords (UDC):	mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;
ID:	18247