for n>0, the nth line increases the number of regions by k iff. it splits k old regions iff. it hits the previous lines in k-1 different points. 由于已有n-1条直线,所以第n条直线最多和已有直线产生n-1个交点,所以k的最大值为n,由此一个可行解,它是充分的 Ln <= Ln-1 + n (n>0)...
A well-known theorem of in plane geometry states that any set of n n non-collinear points in the plane determines at least n n lines. Chen and Chv谩tal asked whether an analogous statement holds within the framework of finite metric spaces, with lines defined using the notion of ...
1.2 Lines in the Plane 我们小时候几乎都遇到过这样的问题:一个西瓜切3刀,最多能切成几块?书里用的例子是Pizza. 【思维方法】平面上已经有n-1条直线,最多把平面分成L(n-1)个区域,如果这n-1条直线互相都不平行,且没有三条直线共点;则第n条直线最多可以和前面的n-1条直线每条都相交(同样没有三条...
In this paper we deal with locating a line in a plane. Given a set of existing facilities, represented by points in the plane, our objective is to find a straight line l minimizing the sum of weighted distances to the existing facilities, or minimizing the maximum weighted distance to the...
As shown in the diagrams below, if the three lines are all parallel, then the plane is divided into four regions; if two of the lines are parallel and the third line intersects them, then the plane is divided into six regions; and if none of the lines are parallel to one another, th...
random lines in the plane defined by their slope and distance from the origin. The slope is uniformly distributed on [0, 2π] and indepe... L Devroye,G Toussaint - 《Journal of Algorithms》 被引量: 25发表: 1993年 New algorithm for constructing dynamic convex hull in the plane An ...
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英语翻译which of the following lines in the xy-plane does not contain any point with intergers as both coordinates? 答案 以下xy平面内的哪条线不包含任何一个xy坐标都为整数的点相关推荐 1英语翻译which of the following lines in the xy-plane does not contain any point with intergers as both co...
Descriptive set theory.The purpose of this paper is to give some natural examples of Borel-inseparable pairs of coanalytic sets in Polish spaces. A ... Becker,Howard - 《Mathematika》 被引量: 26发表: 1986年 Absorbing sets for n-dimensional spaces in absolute Borel and projective classes Absor...
Find the equation of a plane containing P_0=(1,2,3) and perpendicular to n=[1,-1,2] . Solution: (x-1)-(y-2)+2(z-3)=0\Rightarrow x-y+2z=5 3.3 The line of intersection of two planes Example Find a vector tangent to the line of intersection of the planes Solution: We ...