Wonderful Points of the Triangle. Singular Point of Morley’s Theorem
T. P. Malyutina, N. S. Leonov, A. S. Shiptenko
Donbas National Academy of Civil Engineering and Architecture
Abstract: The article is devoted to the consideration of the graphical algorithm for defining the main remarkable points of the triangle: Apollonius, Spiker, Gergonne, Nagel, which also include points that are isotomically conjugate with them, for example, the Lemoine point. An example of specifying the singular point of Morley’s theorem (the theorem on the intersection of trisectrices) is proposed. Based on the methods of parametrizing geometric shapes, a number of relations are obtained for deriving the equation of this singular point. The basis for obtaining it was the O-theorem (the main theorem of BN-calculus), which made it possible to find the center of an equilateral Morley triangle – the intersection point of the lines connecting the vertices of a given triangle with the opposite vertices of the Morley triangle.
Keywords: remarkable points of a triangle, point (BN-) calculus, isogonal and isotomic conjugation, Cheva’s theorem, сheviana, a singular point of Morley’s theorem, trissector, angular parametrization.
Pages: 50-56.
Link for citation: Malyutina, T. P.; Leonov, N. S.; Shiptenko, A. S. Wonderful Points of the Triangle. Singular Point of Morley’s Theorem. – Text : electronic. – In: Proceeding of the Donbas National Academy of Civil Engineering and Architecture. – 2021. – Issue 2021-4(150) Scientific and technical achievements of students of the construction and architectural industry. – Р. 50-56. – URL: https://donnasa.ru/publish_house/journals/vestnik/2021/2021-4(150)/st_10_malyutina_leonov_shiptenko.pdf (date of access: 15.10.2024). (in Russian)
Issue 2021-4 (150)Journal: Proceeding of the Donbas National Academy of Civil Engineering and Architecture
Publish house: Donbas National Academy of Civil Engineering and Architecture