论文标题
三角锥和立方体
Triangle conics and cubics
论文作者
论文摘要
这是一篇有关经典几何形状中三角形立方体和圆锥体的论文，并具有投射几何形状的元素。近年来，新泽西州·怀尔德伯格（N.J. Wildberger）使用代数观点积极处理该主题。 H.M.还详细研究了三角锥。 Cundy和C.F.最近帕里。本文的主要任务是开发一种用于创建曲线的算法，该曲线通过三角形中心。在研究期间，注意到一些不同的三角形中心以不同的三角形重合。最简单的例子是：基本三角形中的一种获取器是偏心三角形中的矫形器。这是创建算法的关键。确实，我们可以将属于一个曲线（基本曲线）的点与另一个三角形的其他点匹配。因此，我们得到了一个新的交织几何对象。在研究期间，有许多新的三角锥和立方体数量被认为是它们在欧几里得空间中的特性。此外，还讨论了在投射几何形状中获得的定理的推论，证明所有下降结果都可以转移到Projeticve平面上。
This is a paper about triangle cubics and conics in classical geometry with elements of projective geometry. In recent years, N.J. Wildberger has actively dealt with this topic using an algebraic perspective. Triangle conics were also studied in detail by H.M. Cundy and C.F. Parry recently. The main task of the article was to develop an algorithm for creating curves, which pass through triangle centers. During the research, it was noticed that some different triangle centers in distinct triangles coincide. The simplest example: an incenter in a base triangle is an orthocenter in an excentral triangle. This was the key for creating an algorithm. Indeed, we can match points belonging to one curve (base curve) with other points of another triangle. Therefore, we get a new intersting geometrical object. During the research were derived number of new triangle conics and cubics, were considered their properties in Euclidian space. In addition, was discussed corollaries of the obtained theorems in projective geometry, what proves that all of the descovered results could be transfered to the projeticve plane.
