IMO LongList 1967, Socialists Republic Of Czechoslovakia 4
Source: IMO LongList 1967, Socialists Republic Of Czechoslovakia 4
December 16, 2004
geometryperimetersquaredissectiontriangulationIMO ShortlistIMO Longlist
Problem Statement
The square has to be decomposed into triangles (which are not overlapping) and which have all angles acute. Find the smallest integer for which there exist a solution of that problem and for such construct at least one decomposition. Answer whether it is possible to ask moreover that (at least) one of these triangles has the perimeter less than an arbitrarily given positive number.