Theorem 4 . 4 any polygonal dissection of a convex n - gon into a square of the same area requires at least [ ] pieces 4用polygonalcut方法把一个凸n边形分划为等面积的正方形至少需要[ n / 4 ]块。
In the present paper , we discuss the minimum number of pieces needed to dissect a regular m ? gon into a regular n - gon of the same area using glass - cuts and polygonal cuts . we obtain the following results 本文主要讨论分别用两种不同的分划方法- glass - cut分划法和polygonalcut分划法把一个正m边形分划为等面积的正n边形需要的最小块数。
Theorem 4 . 3 the following bound holds for the function g for all sufficiently large non - negative integers m < n : where g ( m , n ) denotes the minimum number of pieces needed to dissect a regular m - gon into a regular n - gon using glass - cuts 3设g ( m , n )表示将一个正m边形分划为等面积的正n边形所需的最小块数,对于足够大的非负整数m n ,下式成立:定理4
An old theorem from the first half of the nineteenth century by lowry , wallace , bolyai and gerwien asserts that any simple polygon can be dissected into a finite number of pieces and put back together to form any other simple polygon of the same area 十九世纪上半叶lowry , wallace , bolyai与gerwien同时证明了一个古老的数学命题:任意给定平面上一个简单多边形,必可将其分划成有限块,重新安排,拼成另一个任意给定的等面积的简单多边形。
According to the observed experiments that the na2feo4 solution with the same concentration and volume were decomposed by the same area of different membrane , we learned the order of the decomposing rate of na2feo4 caused by different membranes : soapnated cellulose acetate > vinylon > polypropylene polyvinyl chloride = polyethylene microfiber glass mat 从观察等面积的隔膜引起同浓度同体积的na _ 2feo _ 4溶液的分解实验可知,不同隔膜材料引起na _ 2feo _ 4溶液分解速率从大到小的顺序是,皂化再生纤维素膜维尼纶无纺布改性聚丙烯膜聚氯乙烯膜辐射接枝聚乙烯膜复合玻璃纤维毡。