Prostorna interpretacija Hugelschaffer-ove konstrukcije jajaste krive

Abstract

Konstrukcija jajaste kubne krive Hügelschäffer-ovom metodom, zasniva se na konstrukciji elipse metodom koncentričnih krugova različitih radijusa, a i b, koji odgovaraju parametrima elipse. Načinjen je pokušaj da se prostornom interpretacijom ovih krugova u bazise konusa I cilindra, objasni vrsta pravoizvodne površi koja bi kao ravan presek imala upravo ovako nastalu zatvorenu jajastu krivu. U pitanju je konoid koji kao jednu vodilju ima pravu, a kao drugu vodilju prostornu presečnu krivu ovih kvadrika.

The construction of the ovoid cubic curve by the Hügelschäffer method is based on the construction of the ellipse by the method of concentric circles of different radii, a and b, which correspond to the parameters of the ellipse. An attempt was made to explain the type of rectilinear surface by the spatial interpretation of these circles into the bases of a cone and a cylinder, which, as a plane section, will have a closed egg curve formed in this way. the rectlinear surface is a conoid that has a straight line as a directrix, and a spatial cross-sectional curve of the above quadrics as the other directrix.