The problem involves determining the maximum number of points that can be placed within an equilateral triangle of side length 2, under the condition that no two points are within a distance of 1 from each other. The discussion centers around the application of the pigeonhole principle in this geometric context.
The discussion is ongoing, with participants exploring different interpretations of the problem and the implications of dividing the triangle into sections. There is a recognition of the need for a formal proof to support claims about the number of points that can be placed, and some guidance has been offered regarding potential configurations.
Participants express confusion regarding certain calculations and the rationale behind them, indicating a need for clarification on the geometric properties involved. The problem's constraints and the specific requirement that no two points be within a distance of 1 are central to the discussion.
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.