Naslov
Nedian triangle of ratio n

Autori
Kodrnja, Iva ; Koncul, Helena

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

Izvornik
Abstracts - 20th Scientific-Professional Colloquium on Geometry and Graphics / Došlić, T. ; Jurkin, E. - Zagreb : Hrvatsko društvo za geometriju i grafiku, 2017, 18-18

Skup
20th Scientific-Professional Colloquium on Geometry and Graphics

Mjesto i datum
Fužine, Hrvatska, 03.09.2017. - 07.09.2017

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Domaća recenzija

Ključne riječi
triangle, cevian, nedian, interior nedian trinagle, isotomic point

Sažetak
We start with a triangle ABC and a number n in R. On each of the sides of a triangle (in a counterclockwise order), we choose the point that divides the side in ratio n such that AC_n/AB=BA_n/BC=CB_n/CA=n and look at the cevians connecting this point and the opposite vertex. These cevians are called nedians with ratio n. Each pair of the three nedians intersect at a point creating a triangle A_1B_1C_1 called (interior) nedian triangle of ratio n. Using analytic geometry we can find ratios of perimeters, areas, side-lengths etc of this triangle. If we vary the parameter n, we can observe the locus of the vertices of the nedian triangle or its triangle points. We show that this locus lies on the self-isotomic ellipses of the triangle ABC. Furthermore, for a given triangle ABC and a fixed number n we can repeat the construction of the nedian triangle of ratio n on the triangle A_1B_1C_1 and so on. We will analyse properties of these iteration.

Izvorni jezik
Engleski

POVEZANOST RADA