MathDB

Lots of isosceles triangles

Source: Brazilian Math Olympiad 2006, Problem 2

October 30, 2006

combinatorics unsolvedcombinatorics

Problem Statement

Let

n

be an integer,

n \geq 3

. Let

f(n)

be the largest number of isosceles triangles whose vertices belong to some set of

n

points in the plane without three colinear points. Prove that there exists positive real constants

a

and

b

such that

an^{2}< f(n) < bn^{2}

for every integer

n

n \geq 3