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Two lines and two circles are equivalent

Source: ISI (BS) 2008 #10

May 4, 2012
functiontopologygeometrygeometric transformationreflectionhomothetyalgebra unsolved

Problem Statement

Two subsets AA and BB of the (x,y)(x,y)-plane are said to be equivalent if there exists a function f:Aā†’Bf: A\to B which is both one-to-one and onto. (i) Show that any two line segments in the plane are equivalent. (ii) Show that any two circles in the plane are equivalent.
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