Problem 1. It is true that it is possible to put positive numbers at the vertices of a triangle so that the sum of two numbers at the ends of each side is equal to the length of the side?
This looks like a simple linear algebra question with three variables and three equations. But it has a pretty geometrical solution. What is it?
Problem 2. Prove that it is possible to assign a number to every edge of a tetrahedron so that the sum of the three numbers on the edges of every face is equal to the area of the face.
Again we have six sides and four faces. There should be many solutions. Can you find a geometric one?Share: