Apr 23, 2010
Do you believe in what you see? -- Visual Proofs in Mathematics
When you see a nice painting from a famous artist, you really have to focus on it in order to fully appreciate its beauty and harmony it encompasses. Mathematics is no different. When a sketch, a graph or a chart is given to you depicting mathematical ideas, you have to focus on it in order to grasp its meaning. Mathematical statements can be represented and proved visually this way enhancing our understanding of the matter. This is a continuation of previous lectures about mathematical proofs without words!
We will discuss some properties of the triangular numbers.
Triangular numbers: sum of the first n natural numbers: