Mathematics
Newton's Method for Root Finding with Convergence Analysis
Quick fact
Newton's method can double the number of correct digits at each iteration when started near a simple root, a property called quadratic convergence—making it far faster than many other root-finding methods.
Why this is interesting
You probably know that many equations can't be solved exactly. But what if you could guess the answer and then use a simple rule to improve that guess—sometimes doubling the number of correct digits with each step?