# Edit Create an Image Page: Inversion

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 Image Title*: Upload a Math Image This image is an example of a fractal pattern that can be created with repeated inversion in circles. Inversion is a type of transformation that moves points from the inside of a circle to the outside and from the outside of a circle to the inside using a specific rule. It can be used to create images such as the one on this page, but more importantly it can be used to simplify certain proofs. Inversion is also a method for understanding and solving the [[Problem of Apollonius]]
file=PointInversion2D.swf‎ == Important Properties == [[Image:InversePoints.gif|thumb|350px|Image by:[http://mathworld.wolfram.com/Inversion.html MathWorld]|right]]In the diagram we can see other properties of inversion as well. For example: :* Q is a point on the circle such that OQ is perpendicular to PQ :* P' is the foot of the altitude of the triangle OQP where QP' is perpendicular to OP :*We can now see that triangle OP'Q is similar to triangle OQP From these properties we are able to deduce the equation [itex](OP)/k=k/(OP')[/itex] which is equivalent to our first equation: [itex] Algebra Analysis Calculus Dynamic Systems Fractals Geometry Graph Theory Number Theory Polyhedra Probability Topology Other None Algebra Analysis Calculus Dynamic Systems Fractals Geometry Graph Theory Number Theory Polyhedra Probability Topology Other None Algebra Analysis Calculus Dynamic Systems Fractals Geometry Graph Theory Number Theory Polyhedra Probability Topology Other Yes, it is.