|
Search: id:A121505
|
|
|
| A121505 |
|
Hit triangle for unit circle area (pi) approximation problem described in A121500. |
|
+0
1
|
|
| 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; listen)
|
|
|
OFFSET
|
3,1
|
|
|
COMMENT
|
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.
|
|
LINKS
|
W. Lang: First rows.
|
|
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.
|
|
EXAMPLE
|
[1], [0,0], [0,1,0], [0, 0, 1, 0], [0, 0, 0, 0, 0], [0, 0, 0, 1, 0,
0],...
|
|
CROSSREFS
|
Sequence in context: A120524 A014177 A014129 this_sequence A014289 A015297 A015073
Adjacent sequences: A121502 A121503 A121504 this_sequence A121506 A121507 A121508
|
|
KEYWORD
|
nonn,tabl,easy
|
|
AUTHOR
|
Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Aug 16 2006
|
|
|
Search completed in 0.002 seconds
|
