The Box Principle or also known as the Postman Principle is a classic theorem of mathematics which is used to develop other theorems, especially in the field of “cordinatoria” theory, set theory and real numbers theory. This article illustrates the proof of the principle argued by Dr. Yu Takeuchi in his lecture at the First National and Third Regional Meeting Natural Science Teaching Conference hosted by the Universidad Católica Popular de Risaralda in October 2009. It also provides some important applications of this theorem.