On Umbilic Axes of Circles of the Non Cyclic Quadrangle in the Isotropic Plane (CROSBI ID 164560)
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Šimić, Marija ; Volenec, Vladimir ; Beban-Brkić Jelena
engleski
On Umbilic Axes of Circles of the Non Cyclic Quadrangle in the Isotropic Plane
A power of the point and a power of the line with respect to the circle in the isotropic plane are studied in this paper. To begin with, the radical axis and the radical center of circles in the isotropic plane are presented. As the principle of duality is preserved in the isotropic plane, notions dual to the radical axis and to the radical center, the umbilic point and the umbilic axis are introduced. Non cyclic quadrangle is called standard if a special hyperbola with the equation xy = 1 is circumscribed to it. The properties of the standard quadrangle related to the umbilic point and the umbilic axis are given.
Isotropic plane; Radical center; Radical axis; Umbilic point; Umbilic axis
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