Formalising the use of the centre of mass method in mathematical problems

Meirav Amram, Miriam Dagan, Sagi Levi, Artour Mouftakhov

In this paper, we adopt from physics the concept of centre of mass and use it in the solution of classical geometric problems. Such uses include finding both the incentre and orthocentre of a triangle. We define the concept of centre of mass mathematically and show how to formalise the intuitive solution from physics into a formal mathematical solution. This concept is easy to teach because it requires only basic knowledge of vectors; it can help in solving many complicated geometrical problems.