What is the most efficient rectangle

   

It has been suggested that the content of this page should be merged with TheLargestAreaSamePerimeter.


It has been suggested that the content of this page should be merged with TheLargestAreaSamePerimeterTest.


Alex Weldon: I think it's worth noting that, when building on the side, you get one side (the edge of the goban) for free. So then the most efficient shape is a rectangle of width twice its height, not a square (in the corner, you have two sides, so a square is better).

[Diagram]

Build rectangles on the side.

White has actually invested one stone more than Black (19 vs. 18), but Black has 32 points of territory to White's 30. Because the side of the board forms one side of the territory, stones played to increase width count more than stones played to increase height (unless the width is already much greater than the height). Perhaps that's why it's often better to extend along the third or fourth line in the opening and early middle game, rather than building one's moyos upwards. Of course, the fact that territory built higher up is easier to reduce and harder to defend is also important.

[Diagram]

1 stone difference


Bill: In one of his books, Ishida Yoshio repeats the argument in an article in Kido by a mathematician, who claimed, based upon efficient rectangles, that running along the third line (under the opponent's stones on the fourth line) for more than 6 points is inefficient.


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