Feedback | SoME

The Method of Moving Points

Audience:

Tags: geometryolympiadproblem-solving-method

Geometry problems in math competitions can feel impossible, but what if there was a cheat code? In this video, I introduce the Method of Moving Points, a powerful problem solving technique that helped me solving every geometry problem on every contest I had in my last year of competing. The basic concepts of the method are internationally known, however this alone is not enough to solve hard problems. That's why I made an extension of the method, with which the hardest problems can be solved too. In this video I explain the basic version of the method, and demonstrate it on an example problem from the IMO. I made a document containing the extended version, which can be found in the description.

Analytics

4.9 Overall score*

122 Rank

8 Votes

5 Comments

Comments

I think the topic is interesting.

However, the introduction is a bit unclear, and it is very fast !

5.4

This is the first time I have heard of this method of moving points. It would have helped to have some simpler demonstrations of the method before the example from the maths olympiad to really get a full understanding.

I was able to follow almost everything in the video, but I wish that it slowed down a bit to let the explanations sink in, especially at the end when there were 15 different lines and points to keep track of. It would also have been nice to start with an example of a geometric problem, so that while learning about the moving points method, we have an application in the back of our mind to motivate it.

I wasn’t familiar with the projective plane before this video, so it was interesting to see the algebraic descriptions of points and lines - although I wanted more geometric visualizations on the projective plane, because I had trouble visualizing how the three coordinates (x,y,z) corresponded to lines or points in the plane. But that’s probably for a separate video which just introduces the projective plane.

Overall, I would be interested in a series which covers the projective plane/homogenous coordinates and the polynomial degree proofs in more depth - this video definitely convinced me of the power of the method, but it seems like it requires too much working-up to fit in a single video.

4.5

What is presented is a very advanced method for the average student, but it can be useful for the more talented ones. It is a technique widely used by mathematicians; there is not much originality, and it lacks aids for memorization.

Very nice video. I had heard about the method, but needed these visualizations for understand it :)