crta
Hrvatska znanstvena Sekcija img
bibliografija
3 gif
 Naslovna
 O projektu
 FAQ
 Kontakt
4 gif
Pregledavanje radova
Jednostavno pretraživanje
Napredno pretraživanje
Skupni podaci
Upis novih radova
Upute
Ispravci prijavljenih radova
Ostale bibliografije
Slični projekti
 Bibliografske baze podataka

Pregled bibliografske jedinice broj: 837998

Zbornik radova

Autori: Šimić Horvath, Marija; Jurkin, Ema; Volenec, Vladimir; Beban-Brkić, Jelena
Naslov: On Brocard Points of Harmonic Quadrangle in I_2(R)
( On Brocard Points of Harmonic Quadrangle in I_2(R) )
Izvornik: Abstracts − 19th Scientific-Professional Colloquium on Geometry and Graphics, Starigrad- Paklenica, September 4 – 8, 2016 / Došlić, Tomislav ; Jurkin, Ema (ur.). - Zagreb :
Skup: 19th Scientific-Professional Colloquium on Geometry and Graphics
Mjesto i datum: Starigrad-Paklenica, Hrvatska, 04-08.09.2016.
Ključne riječi: isotropic plane ; harmonic quadrangle ; Brocard points
( isotropic plane ; harmonic quadrangle ; Brocard points )
Sažetak:
In this talk we present several results concerning the geometry of a harmonic quadrangle in the isotropic plane I_2(R). We consider the standard cyclic quadrangle with the circumscribed circle given by y = x^2 and the vertices 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 different real numbers, a < b < c < d. The harmonic quadrangle in the isotropic plane is a standard cyclic quadrangle with a special property: vertices A, B, C, and D are chosen in a way that tangents A and C at the vertices A and C, respectively, intersect 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. We show that there exist a unique point P_1, so-called the first Brocard point, such that the lines P_1A, P_1B, P_1C, and P_1D form equal angles with the sides AB, BC, CD and DA, respectively. Similarly, the second Brocard point is defined as the point such that the lines P_2A, P_2B, P_2C, and P_2D form equal angles with the sides AD, DC, CB, and BA, respectively. We compare the obtained results with their Euclidean counterparts.
Vrsta sudjelovanja: Predavanje
Vrsta prezentacije u zborniku: Sažetak
Vrsta recenzije: Nema recenziju
Izvorni jezik: eng
Kategorija: Ostalo
Znanstvena područja:
Matematika
Upisao u CROSBI: Marija Šimić Horvath (marija.simic@arhitekt.hr), 11. Lis. 2016. u 13:16 sati



  Verzija za printanje   za tiskati


upomoc
foot_4