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Antti H S Laaksonen 2017-02-20 23:23:10 +02:00
parent d4ea994907
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luku29.tex
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@ -527,7 +527,7 @@ For example, the area of the polygon
\end{tikzpicture}
\end{center}
is
\[\frac{|(2\cdot5-4\cdot5)+(5\cdot3-5\cdot7)+(7\cdot1-3\cdot4)+(4\cdot3-1\cdot4)+(4\cdot4-3\cdot2)|}{2} = 17/2.\]
\[\frac{|(2\cdot5-5\cdot4)+(5\cdot3-7\cdot5)+(7\cdot1-4\cdot3)+(4\cdot3-4\cdot1)+(4\cdot4-2\cdot3)|}{2} = 17/2.\]
The idea in the formula is to go through trapezoids
whose one side is a side of the polygon,
@ -565,7 +565,7 @@ all such trapezoids, which yields the formula
Note that the absolute value of the sum is taken,
because the value of the sum may be positive or negative
depending on whether we walk clockwise or counterclockwise
along the perimeter of the polygon.
along the boundary of the polygon.
\subsubsection{Pick's theorem}