Extended minimum-number theorems of cyclic and sextactic points on a plane convex oval
Extended minimum-number theorems of cyclic and sextactic points on a plane convex oval
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凸椭圆平面上循环点和六同点的扩展最小数定理
DOI：
10.1007/bf01174373
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发表时间：
1931
影响因子：
0.8
通讯作者：
S. Mukhopadhaya
中科院分区：
文献类型：
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作者：
S. Mukhopadhaya
凸弧S上的点可以按一定的顺序排列，|我称之为正序，第一个点A和最后一个点B是S的上下端点。S上没有点按顺序重复，A不同于B。弧S是一条连续的直线，并具有下列性质：如果P（1），P（2）……P（n）是任意的。n个不同的点，它们形成凸n边形的顶点。如果P（r）和P（s）是S中的任意两个不同点，P（s）高于P（r），则S中位于P（r）和P（s）之间的所有点都将位于给定的一侧有向线P（r）P（s）的（左侧），以及S的所有其他点，不包括P（r）和P（s），将落在同一直线的相对侧（右侧）。平面上位于AB左边或AB上的所有点将构成S的霍尔平面。
The points of a convex arc S can be arranged in a certain order which we wi| l call the positive order, with a first point A and a last point B, which are the lower and upper extremities of S. No point of S is repeated in the order and A is distinct from B. The arc S is a continuous line and possesses th e following properties: If P (1), P (2)..... P (n) be any. n distinct points in order on S, they form the vertices in order of a convex n-gon. If P (r) and P (s) be any two distinct points of S, P (s) being higher than P (r), then all the points of S which lie between P (r) and P (s) will lie on a given side (left side) of the directed line P (r) P (s), and all other points of S, excluding P (r) and P (s), will fall on the opposite side (right side) of the same directed straight line. All points of the plane which lie on the left of AB or on AB, will constitute the hall-plane of S.