A157650 Number of minimum geometric construction etches with compass of fixed opening and straightedge to find the centroid of n points.

0, 4, 9, 12, 19, 21, 28, 28, 36, 38, 46, 45

Offset

1,2

References

Archimedes, On the equilibrium of planes, 287 BC-212 BC (Proposition 4, Book I).

Jason E. Shields, Archimedes Lemma Variation, February 13, 2009 (unpublished).

Links

Table of n, a(n) for n=1..12.

Tom A. Apostol and Mamikon A. Mnastakanian, Finding Centroids The Easy Way, Math Horizons, September (2000), 7-12.

Mathematics StackExchange, Using a compass of fixed opening and straightedge, what is the shortest way to find the centroid of 10 points?, Aug. 2023.

Example

For n=4, the minimum number of geometric etches to find the centroid of 4 points is 12 using a compass of fixed opening and a straightedge.

Crossrefs

Sequence in context: A348918 A181023 A084789 * A312866 A312867 A312868

Adjacent sequences: A157647 A157648 A157649 * A157651 A157652 A157653

Keyword

nonn,more,hard

Author

Jason E. Shields, Mar 03 2009, Mar 13 2009

Status

approved