A121505 Hit triangle for unit circle area (Pi) approximation problem described in A121500.

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

Offset

3,1

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.

Links

Table of n, a(n) for n=3..83.

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 * A014289 A354030 A015297

Adjacent sequences: A121502 A121503 A121504 * A121506 A121507 A121508

Keyword

nonn,tabl,easy

Author

Wolfdieter Lang, Aug 16 2006

Status

approved