Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
Already signed up?
New to KöMaL?

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