The tie theorems
History and Overview
2014-12-04 v2 Metric Geometry
Abstract
Theorem. There are general position points A, B, C, P on the projective plane. Let A_P be the intersection point of lines AP and BC. Analogously define B_P and C_P. Take any points A_1, B_1, C_1 on AP, BP, CP, respectively. Let W_C be the intersection point of A_1B_P and B_1A_P. Analogously define points W_A and W_B. Then lines CW_C, AW_A and BW_B pass through one point. We also generalize this theorem and find interesting related properties.
Cite
@article{arxiv.1411.5227,
title = {The tie theorems},
author = {Roman Krutowski},
journal= {arXiv preprint arXiv:1411.5227},
year = {2014}
}
Comments
8 pages, 7 figures, in Russian