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Search: id:A003957
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| A003957 |
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Decimal expansion of root of cos x = x. |
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+0
10
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| 7, 3, 9, 0, 8, 5, 1, 3, 3, 2, 1, 5, 1, 6, 0, 6, 4, 1, 6, 5, 5, 3, 1, 2, 0, 8, 7, 6, 7, 3, 8, 7, 3, 4, 0, 4, 0, 1, 3, 4, 1, 1, 7, 5, 8, 9, 0, 0, 7, 5, 7, 4, 6, 4, 9, 6, 5, 6, 8, 0, 6, 3, 5, 7, 7, 3, 2, 8, 4, 6, 5, 4, 8, 8, 3, 5, 4, 7, 5, 9, 4, 5, 9, 9, 3, 7, 6, 1, 0, 6, 9, 3, 1, 7, 6, 6, 5, 3, 1, 8, 4, 9, 8, 0, 1, 2, 4, 6
(list; cons; graph; listen)
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OFFSET
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0,1
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COMMENT
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The unique root of cos(x)=x has been called the Dottie number. This root is a simple nontrivial example of a universal attracting fixed point. The story of how the Dottie number got its name and mathematical concepts relating to this value can be used as teaching tools. Pedagogical examples are given for several courses ranging from Calculus I to Complex Analysis. [Kaplan] - Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 04 2007
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REFERENCES
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Samuel R. Kaplan, The Dottie Number, Math. Magazine, 80 (No. 1, 2007), 73-74.
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LINKS
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Ben Branman (137ben(AT)comcast.net), Apr 12 2008, Table of n, a(n) for n = 0..499
Eric Weisstein's World of Mathematics, Cosine
Eric Weisstein's World of Mathematics, Almost Integer
Eric Weisstein's World of Mathematics, Dottie Number
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EXAMPLE
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0.7390851332151606...
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MATHEMATICA
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RealDigits[ FindRoot[ Cos[x] == x, {x, {.7, 1} }, WorkingPrecision -> 120] [[1, 2] ]] [[1]]
FindRoot[Cos[x] == x, {x, {.7, 1}}, WorkingPrecision -> 500][[1, 2]]][[1]] - Ben Branman (137ben(AT)comcast.net), Apr 12 2008
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CROSSREFS
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Sequence in context: A011330 A093587 A072334 this_sequence A021579 A139788 A093525
Adjacent sequences: A003954 A003955 A003956 this_sequence A003958 A003959 A003960
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KEYWORD
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cons,nonn
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AUTHOR
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Leonid Broukhis (leo(AT)mailcom.com)
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EXTENSIONS
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More terms from David W. Wilson (davidwwilson(AT)comcast.net)
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