Problem A. 695. (April 2017)
A. 695. We are given \(\displaystyle 2k\) lines, \(\displaystyle e_1, \ldots, e_{2k}\) in a plane \(\displaystyle S\), further given a line \(\displaystyle g\) which has an angle \(\displaystyle \alpha\) with \(\displaystyle S\). Show that the sum of the pairwise angles between the lines \(\displaystyle e_1, \ldots,e_{2k}, g\) is at most
\(\displaystyle (k^2+k)\cdot \dfrac \pi 2 + k\alpha. \)
(5 pont)
Deadline expired on May 10, 2017.
Statistics:
9 students sent a solution. 5 points: Baran Zsuzsanna, Gáspár Attila, Imolay András, Matolcsi Dávid, Szabó Kristóf, Williams Kada. 4 points: Schrettner Jakab. 3 points: 1 student. 0 point: 1 student.
Problems in Mathematics of KöMaL, April 2017