The definition of inversion Suppose that C is a circle, centre O, radius r, and that P is a point other than O. Then the inverse of P with respect to C is the point P' such that P' lies on OP P and P' lie on the same side of O OP.OP' = r2. We shall denote the inverse of P by iC(P), or, if the circle is obvious, by P'.	Basic Properties P=P' if and only if P is on C. P is inside C if and only if P' is outside C. iC has order 2, i.e. (P')' = P. iO is undefined. There is no point P with iP = O.
Inversion is built into Cabri. This CabriJava window allows you to experiment with inversion in the blue circle. As you drag the point P, watch what happens to the inverse point P'. You can also vary the circle by dragging the centre or a point on the perimeter.
If D is a plane curve, then we can invert each point of D to obtain the inverse curve iC(D). This Cabrijava window shows inversion in the blue circle C. As you move the point P on the red curve, its inverse P' traces out the green curve. You can move the circle by dragging its centre or a point on the perimeter.

Main Inversive Page

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Main Cabri Page