The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A256060 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A256060

Queen Dido's puzzle (the founding of Carthage): a(n) is twice the maximal area of a polygon with 1) vertices on integral Cartesian coordinates, 2) no two edges parallel, and 3) all edge lengths less than or equal to n^2.
(history; published version)

#21 by Joerg Arndt at Mon Feb 18 02:09:53 EST 2019

STATUS

proposed

approved

#20 by Michel Marcus at Mon Feb 18 00:40:08 EST 2019

STATUS

editing

proposed

#19 by Michel Marcus at Mon Feb 18 00:40:03 EST 2019

KEYWORD

nonn,more,changed

STATUS

proposed

editing

#18 by Jon E. Schoenfield at Sun Feb 17 23:03:27 EST 2019

STATUS

editing

proposed

#17 by Jon E. Schoenfield at Sun Feb 17 23:03:23 EST 2019

NAME

Queen Dido's puzzle (the founding of Carthage): a(n) is double twice the maximal area of a polygon with 1) vertices on integral Cartesian coordinates, 2) no two edges parallel, and 3) all edge lengths less than or equal to n^2.

COMMENTS

An optimal polygon will always be convex. - _Gordon Hamilton._

For parity reasons, the edges of the maximal-area polygon are not always as long as possible. This is true for a(9) through a(12). - _Gordon Hamilton._

EXAMPLE

a(4) = 2 because this triangle has area 1 (remember a(n) is double twice the area):

STATUS

approved

editing

#16 by N. J. A. Sloane at Tue Mar 17 02:11:17 EDT 2015

STATUS

editing

approved

#15 by N. J. A. Sloane at Tue Mar 17 02:11:13 EDT 2015

COMMENTS

These values are have not proven been proved to be optimal.

STATUS

proposed

editing

#14 by Gordon Hamilton at Tue Mar 17 01:04:12 EDT 2015

STATUS

editing

proposed

#13 by Gordon Hamilton at Tue Mar 17 01:04:06 EDT 2015

COMMENTS

For parity reasons, the edges of the maximal-area polygon are not always as long as possible. This is true for a(9) through a(12). - Gordon Hamilton.

#12 by Gordon Hamilton at Tue Mar 17 01:03:04 EDT 2015

COMMENTS

An optimal polygon will always be convex. - Gordon Hamilton.

For parity reasons, the edges of the maximal-area polygon are not always as long as possible. This is true for a(9) through a(12).

STATUS

proposed

editing