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Diagonal Triangle of a Non Tangential Quadrilateral in an Isotropic Plane


Šimić, Marija; Beban-Brkić, Jelena
Diagonal Triangle of a Non Tangential Quadrilateral in an Isotropic Plane // Abstracts of the 4th Croatian Mathematical Congress / Scitovski, Rudolf (ur.).
Osijek: Croatian Mathematical Society, 2008. str. xx-xx (predavanje, domaća recenzija, sažetak, znanstveni)


Naslov
Diagonal Triangle of a Non Tangential Quadrilateral in an Isotropic Plane

Autori
Šimić, Marija ; Beban-Brkić, Jelena

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

Izvornik
Abstracts of the 4th Croatian Mathematical Congress / Scitovski, Rudolf - Osijek : Croatian Mathematical Society, 2008, Xx-xx

Skup
Croatian Mathematical Congress (4 ; 2008)

Mjesto i datum
Osijek, Hrvatska, 17.-20.06. 2008

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Domaća recenzija

Ključne riječi
Isotropic plane ; Non tangential quadrilateral ; Focus ; Median ; Diagonal triangle
(Isotropic plane ; non tangential quadrilateral ; focus ; median ; diagonal triangle)

Sažetak
Properties of the non tangential quadrilateral ABCD in the isotropic plane are studied in this talk. A quadrilateral is called standard if a parabola with the equation x = y^2 is inscribed in it. Every non tangential quadrilateral can be represented in the standard position. In order to prove the properties of any non tangential quadrilateral, it is sufficient to prove the properties for the standard quadrilateral. The notions of the focus and the median of the quadrilateral are introduced and coordinates of the vertices and the equations of the sides of its diagonal triangle are given. It is shown that the midlines of the diagonal triangle touch the inscribed parabola of the quadrilateral. Furthermore, quadrilaterals formed by two diagonals and some two sides of the non tangential quadrilateral ABCD are studied and a few theorems on its foci are presented.

Izvorni jezik
Engleski

Znanstvena područja
Matematika



POVEZANOST RADA


Ustanove
Geodetski fakultet, Zagreb,
Arhitektonski fakultet, Zagreb