Newton’s Method Introduction Sir Isaac Newton is famous for many discoveries in both math and science. From gravity to calculus, Newton made many fundamental breakthroughs that have shaped thought for centuries and are still in use today. For this reason, Newton has always been one of the most interesting characters in history for me and thus is why I found such great interest in his theories and being able to explore them further. However, though he had countless monumental breakthroughs, he also had other theories that are not as well known, which interested me even more as they are not discussed as much in school. One such theory is Newton’s method for approximating the zeroes of a function, which is simply known as Newton’s Method. This method is a unique approach for approximating zeroes due to its use of several iterations of a formula to slowly grow closer and closer to the zero. The aim of this paper is to investigate the use and accuracy of Newton’s Method to approximate the zeroes of a function. This investigation aims to explore the history of the method and possible influences to Newton’s discovery, the basic mechanics of the method such as how and when it works, and finally Newton’s method will be compared to the most conventional means of determining the zeroes of function which are the algebraic formulas like the quadratic formula. History Although it was Newton who would eventually be credited with the discovery of a method for finding the roots of a

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