### Some articles on *apollonius, problem, apollonius problem*:

Problem Of Apollonius - Special Cases - Mutually Tangent Given Circles: Soddy's Circles and Descartes' Theorem

... If the three given circles are mutually tangent,

... If the three given circles are mutually tangent,

**Apollonius**'**problem**has five solutions ... This special case of**Apollonius**'**problem**is also known as the four coins**problem**... The three given circles of this**Apollonius problem**form a Steiner chain tangent to the two Soddy's circles ...Problem Of Apollonius - Solution Methods - Algebraic Solutions

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**Apollonius**'**problem**can be framed as a system of three equations for the center and radius of the solution circle ... suggest (incorrectly) that there are up to sixteen solutions of**Apollonius**'**problem**... Therefore,**Apollonius**'**problem**has at most eight independent solutions (Figure 2) ...Problem Of Apollonius - Applications

... The principal application of

... The principal application of

**Apollonius**'**problem**, as formulated by Isaac Newton, is hyperbolic trilateration, which seeks to determine a position from the differences in distances to ... Solutions to**Apollonius**'**problem**were used in World War I to determine the location of an artillery piece from the time a gunshot was heard at three different positions, and hyperbolic ... This multilateration**problem**is equivalent to the three dimensional generalization of**Apollonius**'**problem**and applies to global positioning systems such as GPS ...Problem Of Apollonius

... In Euclidean plane geometry,

... In Euclidean plane geometry,

**Apollonius**'s**problem**is to construct circles that are tangent to three given circles in a plane (Figure 1) ...**Apollonius**of Perga (ca. 190 BC) posed and solved this famous**problem**in his work Ἐπαφαί (Epaphaí, "Tangencies") this work has been lost, but a 4th-century report of his results by Pappus of Alexandria has survived ...Problem Of Apollonius - Special Cases - Number of Solutions

... The

... The

**problem**of counting the number of solutions to different types of**Apollonius**'**problem**belongs to the field of enumerative geometry ... The general number of solutions for each of the ten types of**Apollonius**'**problem**is given in Table 1 above ... For illustration,**Apollonius**'**problem**has no solution if one circle separates the two (Figure 11) to touch both the solid given circles, the solution circle would have to cross the dashed given circle but ...### Famous quotes containing the word problem:

“A curious thing about the ontological *problem* is its simplicity. It can be put in three Anglo-Saxon monosyllables: ‘What is there?’ It can be answered, moveover, in a word—‘Everything.’”

—Willard Van Orman Quine (b. 1908)

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