engleski

Inversion of degree n+2

In this paper, by the method of synthetic geometry, we define the transformation of three-dimensional projective space where corresponding points lie on the rays of the 1st order, n-th class congruence $C_n^1$ and are conjugate with respect to proper quadric $\Psi$. We prove that this transformation takes a straight line to the (n+2) order space curve and a plane to the (n+2) order surface which contains n-ple straight line. It is shown that in Euclidean space the pedal surfaces of congruences $C_n^1$ can be obtained by this transformation. The analytical approach enables visualizations of the resulting curves and surfaces and they are given in four examples.

congruence of lines; inversion; $n$th order algebraic surfaces with $(n-2)$-ple line; pedal surfaces of congruences

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