A Complete Quadrilateral in Rectangular Coordinates

Scientific paper - Review paper

• Title (croatian): Potpuni četverostran u pravokutnim koordinatama
• Author: Vladimir Volenec
• Author: Ema Jurkin
• Author: Marija Šimić Horvath
• Author's institution: University of Zagreb; Faculty of Architecture
• Author's institution: University of Zagreb; Faculty of Science; (Department of Mathematics)
• Author's institution: University of Zagreb; Faculty of Mining, Geology and Petroleum Engineering; (Department of Mathematics, Informatics and Descriptive Geometry)
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract (english)

A complete quadrilateral in the Euclidean plane is studied. The geometry of such quadrilateral is almost as rich as the geometry of a triangle, so there are lot of associated points, lines and conics. Hereby, the study was performed in the rectangular coordinates, symmetrically on all four sides of the quadrilateral with four parameters a, b, c, d. In this paper we will study the properties of some points, lines and circles associated to the quadrilateral. All these properties are well known, but here they are all proved by the same method. During this process, still some new results have appeared.

Abstract (croatian)

U radu proučavamo potpuni četverostran u euklidskoj ravnini. Poput trokuta i potpuni četverostran ima mnogo zanimljivih svojstava te pridruženih točaka, pravaca i konika. Ovdje je proučavanje provedeno korištenjem pravokutnih koordinata, simetrično po sve četiri stranice četverostrana s četiri parametra a, b, c, d. Proučavamo svojstva točaka, pravaca i kružnica pridruženih četverostranu. Gotovo sve tvrdnje prikazane u ovom radu su dobro poznate, ali su se ipak ponegdje usput pojavili i neki novi rezultati.

• Keywords (english): Euclidean plane; complete quadrilateral; parabola
• Keywords (croatian): euklidska ravnina; potpuni četverostran; parabola
• Language: english
• Language: croatian
• Publication type: Scientific paper - Review paper
• Publication status: Published
• Peer review: Peer review - international
• Publication version: Published version
• Journal title: KoG
• Numbering: vol. 26, no. 26, pp. 62-78
• p-ISSN: 1331-1611
• e-ISSN: 1846-4068
• DOI: https://doi.org/10.31896/k.26.6
• URN:NBN: urn:nbn:hr:169:778775
• Publication: 2022
• Document URL: https://hrcak.srce.hr/288264
• Type of resource: Text
• Access conditions: Open access
• Created on: 2024-02-05 09:50:07