Diophantine Steiner triples and Pythagorean-type triangles

Abstract

V članku predstavimo povezavo med diofantskimi Steinerjevimi trojicami (trojicami naravnih števil, ki so povezane s konfiguracijo dveh disjunktnih krogov, od katerih večji vsebuje manjšega, pri kateri nastopi sklenjena Steinerjeva veriga) in trikotniki s celoštevilskimi stranicami in kotom 60°, 90° ali 120°. Dokažemo povezovalno formulo in jo geometrijsko interpretiramo.

Keywords

matematika;diofantske Steinerjeve trojice;Steinerjev porizem;pitagorejski trikotniki;trikotniki pitagorejskega tipa;mathematics;Diophantine Steiner triples;Steiner porism;Pythagorean triangles;Pythagorean-type triangles;

Data

Language:	English
Year of publishing:	2010
Typology:	1.01 - Original Scientific Article
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
UDC:	514.112:511
COBISS:	15669337
ISSN:	1534-1178
Views:	820
Downloads:	47
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Unknown
Secondary title:	Diofantske Steinerjeve trojice in trikotniki pitagorejskega tipa
Secondary abstract:	We present a connection between Diophantine Steiner triples (integer triples related to configurations of two circles, the larger containing the smaller, in which the Steiner chain closes) and integer-sided triangles with an angle of 60, 90 or 120 degrrees. We introduce an explicit formula and provide a geometrical interpretation.
URN:	URN:SI:UM:
Type (COBISS):	Not categorized
Pages:	str. 93-97
Issue:	ǂVol. ǂ10
Chronology:	2010
ID:	68616