Pappus theorem
When we attended a summer camp when we was in grade 5, there was a day called the Mathematical Day. One of the most memorable experiments was something related to
Geometry:
6 people were split into two teams. Each team stood on one line and the two lines intersected each other. Let’s call two teams A and B. 1rst person in team A was connected to the 2nd person and 3rd person in team B and the same with two other positions and team B with ropes. One interesting fact is that with the naked eye, the three intersections always seemed to be linear as we changed our position as long as we still had to maintain our order. However, my head teacher said that we were not able to prove it with primary knowledge.
When I got into grade 9, that model was again represented but this time on chalkboard: The Pappus theory. So I will present it below now:
Given (A,B,C) and (X,Y,Z) are three points that stayed on both lines in that order. The 3 intersections of (AY,BX), (AZ,CX), (BZ,CY).
The proof is easy to find on the internet and most of them are similar: using Menelaus Theorem to prove. You can search for "Pappus Theorem proof" and the first article from the Department of Math from University of Chicago also provides how Pappus Theorem works in projective space.