auk411 said:I know that there are at least 3. Visually, if you sketch the triangle it looks like there will be a 4. However, I don't know how to prove this.
willem2 said:divide the triangle in 4 area's that can only contain 1 point each
auk411 said:Yes. I'm asking how does one show this. I don't know how to show this. Someone who claims to have the right answer told me that we need to add root 3 over 2 plus root 3 over 6 to get about 1.3.
I am completely lost as to how this is an answer.
The Pigeon Hole Principle is a mathematical concept that states that if there are more pigeons than pigeon holes, at least one pigeon hole must contain more than one pigeon.
The Pigeon Hole Principle is used to prove the existence of a solution to a problem. It works by considering the number of "pigeons" (items or elements) and the number of "pigeon holes" (categories or options), and showing that there must be at least one category with more than one item.
The "Equilateral Triangle Points" problem involves finding the minimum number of points needed to form an equilateral triangle when each point is connected to every other point. It is a classical example of applying the Pigeon Hole Principle.
The Pigeon Hole Principle can be applied by considering the vertices of the equilateral triangle as "pigeon holes" and the points as "pigeons". By showing that there must be at least one vertex with more than one point, we can prove that the minimum number of points needed is three.
Yes, the Pigeon Hole Principle has many other applications in various fields such as computer science, cryptography, and graph theory. It can also be used to solve problems in real-life situations, such as scheduling conflicts or distributing resources among a group of people.