I believe it was Newton who first proposed kinetic energy as being proportional to mass times velocity. Liebniz further refined the relationship by stating that the velocity should be squared. That was later confirmed by Willem 'sGravesande and Emilie du Châtelet. The squaring also is a basis for E=mc2. My question is: why squared? I don't deny the correctness of the two relationships, but if fitting an equation to data, I would be both suspicious and intrigued by the fact that the exponent is exactly two. Not 0.976233 or 2.343983 or 3.599992 but exactly 2.000000. If one looks at other equations in physics, things are not so simple or elegant. What is so unique about squaring here? Where does it come from?