Napredna pretraga

On Harmonic Quadrangle in the Isotropic Plane

Šimić Horvath, Marija; Jurkin, Ema; Volenec, Vladimir; Beban-Brkić, Jelena
On Harmonic Quadrangle in the Isotropic Plane // 6th Croatian Mathematical Congress, June 14-17, 2016, Zagreb, Croatia / Hanzer, Marcela (ur.).
Zagreb, 2016. str. 77-77 (predavanje, međunarodna recenzija, sažetak, znanstveni)

Naslov
On Harmonic Quadrangle in the Isotropic Plane

Autori
Šimić Horvath, Marija ; Jurkin, Ema ; Volenec, Vladimir ; Beban-Brkić, Jelena

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

Izvornik
6th Croatian Mathematical Congress, June 14-17, 2016, Zagreb, Croatia / Hanzer, Marcela - Zagreb, 2016, 77-77

Skup
6th Croatian Mathematical Congress

Mjesto i datum
Zagreb, Hrvatska, 14-17.06.2016

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Isotropic plane ; cyclic quadrangle ; harmonic quadrangle

Sažetak
In this talk we present several results concerning the geometry of the harmonic quadrangle in the isotropic plane. We consider the standard cyclic quadrangle with the circumscribed circle given by y = x^2 and vertices are chosen to be A = (a, a^2), B = (b, b^2), C = (c, c^2), and D = (d, d^2), with a, b, c, d being mutually diff erent real numbers, where a < b < c < d. The harmonic quadrangle in the isotropic plane is the standard cyclic quadrangle with a special property: the vertices A, B, C and D are chosen in a way that tangents A and C at the vertices A and C, respectively, are intersected in the point incident with BD, and tangents B and D at the vertices B and D, respectively, are intersected in the point incident with AC. Accordingly, 2(ac + bd) = (a + c)(b + d) follows.

Izvorni jezik
Engleski

Znanstvena područja
Matematika