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%I #23 Aug 16 2023 07:41:59
%S 0,4,9,12,19,21,28,28,36,38,46,45
%N Number of minimum geometric construction etches with compass of fixed opening and straightedge to find the centroid of n points.
%D Archimedes, On the equilibrium of planes, 287 BC-212 BC (Proposition 4, Book I).
%D Jason E. Shields, Archimedes Lemma Variation, February 13, 2009 (unpublished).
%H Tom A. Apostol and Mamikon A. Mnastakanian, <a href="https://www.jstor.org/stable/25678275">Finding Centroids The Easy Way</a>, Math Horizons, September (2000), 7-12.
%H Mathematics StackExchange, <a href="https://math.stackexchange.com/questions/4747866">Using a compass of fixed opening and straightedge, what is the shortest way to find the centroid of 10 points?</a>, Aug. 2023.
%e 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.
%K nonn,more,hard
%O 1,2
%A _Jason E. Shields_, Mar 03 2009, Mar 13 2009
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