What is inversive geometry?
نویسنده
چکیده
Suppose ↵, are concentric. Let a and b denote the radii of ↵ and respectively, and assume a > b. Clearly, such an arrangement of circles i exists only when the centers C1, . . . , Cn of the n circles 1, . . . n are the vertices of a regular n-gon, whose center is the common center O of ↵ and . Consider then a point of tangency T between two circles i and i+1, and the triangle 4OCiT . The edge OT is a tangent to i, and CiT is a radius, so OT ? CiT . Furthermore, `(CiT ) = a b 2 and `(OCi) = a+b 2 , by straightforward geometry. So, we have
منابع مشابه
Non-rigidity of Spherical Inversive Distance Circle Packings
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