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George Chrystal - Algebra_ An elementary textbook, Vol 2 Page 34 Exercise Ⅳ. 12
If any number of closed curves be drawn in a plane each cutting all the others, and if $n_r$ be the number of points through which $r$ curves pass, the number of distinct closed areas formed by the curves is $1+n_{2}+2 n_{3}+\ldots+r n_{r+1}+\ldots$
如果在一个平面上绘制任意数量的封闭曲线，每条封闭曲线都与其他所有曲线相交，并且如果 $n_r$ 是有 $r$ 条曲线通过的点的个数，则由曲线形成的封闭区域的不同面积数为 $1 +n_{2}+2 n_{3}+\ldots+r n_{r+1}+\ldots$ |
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