Posted by Mark on Monday, July 15, 2013 at 4:57pm.
Brilli the ant has a block of cheese that is in the shape of an equilateral triangle. She is hosting a party, and has invited her twolegged house mates. She insists that all of her guests get a piece of cheese that is in the shape of an isosceles triangle. What is the maximal number N such that she cannot split the equilateral triangle block of cheese into N nondegenerate isosceles triangles?

Math  MathMate, Monday, July 15, 2013 at 6:07pm
She cannot subdivide the equilateral triangle into 2 isosceles triangles. This is the smallest N which is impossible.
She can subdivide it into 3 congruent isosceles triangles by joining the centroid with each of the vertices. Each triangle is then 3030120 as angles.
Each of the 3030120 triangles can in turn be subdivided into 3 isosceles triangles with angles 606060, and 3030120, thus adding two more triangles.
So the next possible N are then 5, 7, 9.
Since each of the smaller 3030120 triangles can again be subdivided, indefinitely, we conclude that the original equilateral triangle can be subdivided into odd N above 1. Even N are therefore not possible. Thus there is no maximum number N, since N>∞, as long as N=2k, where k∈integers.

Math  MysteriousPerson, Thursday, July 18, 2013 at 5:37pm
MathMate, I would disagree with you because 4 triangles are possible. We can break up the equilateral triangle to 4 different equilateral triangles.
Answer This Question
Related Questions
 Math  Brilli the ant has a block of cheese that is in the shape of an ...
 physics  Three ants are sitting on the vertices of equilateral triangle of side...
 math  a piece of wire 12 meters long is cut into two pieces.one piece is bent ...
 math  Hector has invited 12 people to his party, 4 of whom are his brothers. IF...
 Math  A piece of wire 12 m long is cut into 2 pieces. One piece is bent into ...
 Math  Phil bought a block of cheese in the shape of a rectangular prism ...
 math  Part 2: Now it’s time to make the guest list! Figure out how many guests ...
 math  Part 2: Now it’s time to make the guest list! Figure out how many guests ...
 math  Part 2: Now it’s time to make the guest list! Figure out how many guests ...
 Math  A piece of wire of 14 meters long is cute into 2 pieces. One piece is ...
More Related Questions