三角形中和cotA + cotB + cotC的面积性质
On an area property of the sum cotA+cotB+cotC in a triangle
摘要：
给定一个三角形ABC，一个新的三角形A 'B'C'可以如下形成：在点A处画一条与AB线垂直的垂线;然后在B处画一条与BC线垂直的垂线，最后在C处画一条与CA线垂直的垂线。在命题1中，我们证明了比值E '/E等于（cotA+cotB+cotC）^2，这是本文的主要结果，这里E'和E分别代表三角形A 'B'C'和ABC的面积。在公设2中，我们证明了当ABC和A 'B'C'是等边三角形时，上述面积比的最小值为3。在公设3中，我们证明了如果我们只考虑那些三角形对（ABC，A' B 'C'），ABC和A 'B'C'都是直角三角形，则上述面积比的最小值为4。
英文摘要：
Given a triangle ABC, a new triangle A'B'C' can be formed as follows: Draw the perpendicular to the line AB at the pointA; then the perpendicular to the line BC at B, and lastly the perpendicular to the line CA at C.the two triangles ABC and A'B'C' are always similar. In Postulate1 we prove that the ratio E'/E is equal to (cotA+cotB+cotC)^2, which is the main result in this work.Here E' and E stand for the areas of the triangles A'B'C' and ABC respectively. In Postulate 2, we show that the above ratio has minimum value 3, which is attained when ABC and A'B'C' are equilateral triangles.In Postulate 3, we show that if we consider only those pairs of triangles (ABC,A'B'C'), with both ABC and A'B'C' being right triangles, then the minimum value of the above ratio of areas, is 4.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
