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Search: id:A062536
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| A062536 |
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Increasing values for the radius of the inner Soddy circle associated with three unequal kissing circles, the four radii of the system forming a primitive quadruple. |
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+0
2
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OFFSET
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1,1
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COMMENT
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A family of non-square values for a(n) may be generated by the formula a(n) = n{(n + 2)^2 + 1 }/2 for n not a multiple of 5. For some values of a(n) which are squares, the three kissing circles share a common external tangent and their radii are related by 1/sqrt(x) = 1/sqrt(y) + 1/sqrt(z).
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LINKS
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Pat Ballew, Soddy's Formula
Thesaurus.maths.org, Soddy's Formula or Descartes' Circle Theorem
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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The inner Soddy circle radius r is explicitly given by 1/r = 1/x + 1/y + 1/z + 2/R with R^2 = xyz/(x + y +z) where x, y, z are the kissing circles' radii and R the radius of the circle orthogonal to the latter three.
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EXAMPLE
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The quadruples (9,28,63,252) and (74,312,481,888) for instance are respectively the 2nd and 7-th primitive solution set (r,x,y,z) satisfying the given explicit formula for r.
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CROSSREFS
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Sequence in context: A000322 A020737 A147401 this_sequence A099213 A146067 A061502
Adjacent sequences: A062533 A062534 A062535 this_sequence A062537 A062538 A062539
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KEYWORD
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more,nonn
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AUTHOR
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Lekraj Beedassy (blekraj(AT)yahoo.com), Jun 25 2001
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