Abstract
Polar curves with respect to proper conics and polar surfaces with respect to proper quadrics are investigated. Polar curves (surfaces) are defined as the envelope of the polar lines (planes) of the points on a given curve (surface) with respect to a quadratic curve (surface). Polar curves and surfaces are collineations of dual curves and surfaces. Polar curves and surfaces with respect to real unit spheres are negative dual curves and surfaces and are obtained as the inverse of the pedal curves and surfaces with respect to the centers of the sphere.
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