The Largest Area Same Perimeter

    Keywords: Strategy, Theory

A sphere has the largest area with the same perimeter. A square is the world champion amongst the rectangles. So, if you want to get a lot of land with minimum number of stones, don't build stripes.


Alex Weldon: This is balanced, however, by the fact that it's easiest to make territory in the corner and along the sides, where you've already got one or two boundaries covered by the sides of the goban. Therefore, your stones running parallel to the edge of the board count double, since any upper bound you make is effectively mirrored by the edge of the board under those stones. Since we're now talking about optimising profit xy with investment x/2 + y, your most efficient shape for building along the edge would be a rectangle twice as wide as it is high. In the corner, however, you've got two edges working for you, so your investment is doubled both ways, so we're talking about a square again.


This is a copy of the living page "The Largest Area Same Perimeter" at Sensei's Library.
(OC) 2005 the Authors, published under the OpenContent License V1.0.
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