A natural setting for problem of Apollonius is inversive geometry.
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For example, Smogorzhevsky develops several theorems of inversive geometry before beginning Lobachevskian geometry.
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Inversion is a conformal transformation, and is the basic operation of inversive geometry.
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In 1926 he wrote a dissertation " Differential Invariants of Inversive Geometry " for his doctoral degree.
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For graduate study, Boyd went to Johns Hopkins University where he studied inversive geometry with Frank Morley.
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Another example concerns inversive geometry as advanced by Ludwig Immanuel Magnus, which can be considered synthetic in spirit.
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Thus inversive geometry, a larger study than grade school transformation geometry, is usually reserved for college students.
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In 1933 he and his son Frank Vigor published the " stimulating volume ", " Inversive Geometry ".
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Inversive geometry has been applied to the study of colorings, or partitionings, of an " n "-sphere.
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The concept is mainly used in inversive geometry, because straight lines and circles have very similar properties in that geometry and are best treated together.
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