if you know the way an object moves—whether it be a toy ball or a giant planet—the differential equation can tell you what kind of force is being applied. (Newton’s triumph was taking the equation that described the force of gravity and figuring out the shapes of the planets’ orbits. People had suspected that the force was proportional to 1/r2, and when ellipses popped right out of Newton’s differential equations, people began to believe that Newton was correct.) Despite the power of calculus, the key problem remained. Newton’s work was based on a very shaky foundation—dividing zero by itself.
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