Saturday, November 27, 2010

More estimates

Last time, I talked about the height of a hexagon; the strategy I used works with any shape with a pair of parallel sides.  The parallel sides allow you to stack the polygons and add up the heights without having to worry about angles. For instance, it will work with a regular octagon.  The picture to the left shows 5 stacked octagons that are slightly more than 12 square (otherwise in TileLand the top purple square would be wiped out).  That means that 5 octagons > 12 squares or that  1 octagon > 12/5 =2.4 (since they are unit squares). 
For those who like to exact lengths, you can break the height of an octagon up into three pieces.  This diagram below demonstrates the breakdown: two half squares of length 1/ root 2  (since the diagonal is 1) and a rectangle with the long side of length 1.  Root 2 plus 1 is 1.41421+1 = 2.41421.   

Look forward to when I tackle odd sided polygons that don't have parallel sides.

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