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A121505
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Hit triangle for unit circle area (pi) approximation problem described in A121500.
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1
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1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 3,1
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COMMENTS
| Record for n=3,4,... only those (n, A121500(n)) pairs which have relative error E(n, A121500(n)) smaller than all errors with smaller n .This produces the table a(n,m).
The unit circle area is approximated by the arithmetic mean of the areas of an inscribed regular n-gon and a circumscribed regular m-gon.
For each row n>=3 the minimal relative error E(n,m):= ((Fin(n) + Fout(m))/2-pi)/ pi) appears for m= A121500(n).
The same hit triangle is obtained when one considers the minimal relative errors for the columns m>=3 and collects the sequence with decreasing errors, starting with m=3.
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LINKS
| W. Lang: First rows.
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FORMULA
| a(n,m)= 1 if m= A121500(n) and E(n,m) < min(E(k,A121500(k)),k=3..n-1), n>=4. a(3,3)=1, else a(n,m)=0.
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EXAMPLE
| [1], [0,0], [0,1,0], [0, 0, 1, 0], [0, 0, 0, 0, 0], [0, 0, 0, 1, 0,
0],...
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CROSSREFS
| Sequence in context: A120524 A014177 A014129 * A014289 A015297 A015073
Adjacent sequences: A121502 A121503 A121504 * A121506 A121507 A121508
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KEYWORD
| nonn,tabl,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Aug 16 2006
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