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ON THE ARC LENGTH UNDER INVERSION
현진오,양창홍 濟州大學校 師範大學 科學敎育硏究所 1993 科學敎育 Vol.10 No.1
Two points P and P' of the plane are said to be inverse with respect to a given circle (0)_(R), if OP·OP'=R^(2) and also if both points are on the same side of O. Circle (O)_(R) is called the circle of inversion and the transformation which sends point P into point P' is known a s an inversion. In this paper we consider the curves in two dimensional Euclidean space R^(Z) and prove that the length of a regular new curve segment β(t) of the inside curve α(t) under inversion is equal to the length of a regular curve segment a(t) by scalar multiple.