Naslov
Some triangle geometry of the triangle family

Autori
Halas, Helena ; Sliepčević, Ana

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
Abstracts, 15th Scientific-Professional Colloquium on Geometry and Graphics / Došlić, T. ; Jurkin, E. - Zagreb : Hrvatsko društvo za geometriju i grafiku, 2011, 16-16

Skup
15th Scientific-Professional Colloquium on Geometry and Graphics

Mjesto i datum
Tuheljske Toplice, Hrvatska, 04.09.2011. - 08.09.2011

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Domaća recenzija

Ključne riječi
Triangle centers; one-parameter family of triangles; envelope of lines; envelope of circles

Sažetak
In this work we consider a one-parameter triangle family T. We prove that the set of the orthocenter, centroid, circumcenter, and some other sets of the triangle centers lie on different hyperbolae. Furthermore, it will be shown that the hyperbolae which are the sets of triangle centers that lie on the Euler lines of the triangle family T have a space interpretation with the Hohenberg transformation. In this presentation we also prove and construct two different cubics as the line envelopes of the side bisectors and Euler lines, and two different quartics as the circle envelopes of the circumcircles and Euler circles of the triangle family T.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA