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In mathematics, an Apollonian gasket or Apollonian net is a fractal generated from triples of circles, where each circle is tangent to the other two. It is named after Greek mathematician Apollonius of Perga. ==Construction== An Apollonian gasket can be constructed as follows. Start with three circles ''C''1, ''C''2 and ''C''3, each one of which is tangent to the other two (in the general construction, these three circles can be any size, as long as they have common tangents). Apollonius discovered that there are two other non-intersecting circles, ''C''4 and ''C''5, which have the property that they are tangent to all three of the original circles – these are called ''Apollonian circles'' (see Descartes' theorem). Adding the two Apollonian circles to the original three, we now have five circles. Take one of the two Apollonian circles – say ''C''4. It is tangent to ''C''1 and ''C''2, so the triplet of circles ''C''4, ''C''1 and ''C''2 has its own two Apollonian circles. We already know one of these – it is ''C''3 – but the other is a new circle ''C''6. In a similar way we can construct another new circle ''C''7 that is tangent to ''C''4, ''C''2 and ''C''3, and another circle ''C''8 from ''C''4, ''C''3 and ''C''1. This gives us 3 new circles. We can construct another three new circles from ''C''5, giving six new circles altogether. Together with the circles ''C''1 to ''C''5, this gives a total of 11 circles. Continuing the construction stage by stage in this way, we can add 2·3''n'' new circles at stage ''n'', giving a total of 3''n''+1 + 2 circles after ''n'' stages. In the limit, this set of circles is an Apollonian gasket. The Apollonian gasket has a Hausdorff dimension of about 1.3057.〔http://abel.math.harvard.edu/~ctm/papers/home/text/papers/dimIII/dimIII.pdf〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Apollonian gasket」の詳細全文を読む スポンサード リンク
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