Born on January 4th, 1643, Isaac Newton was a highly accomplished mathematician and physicist; over a period of two years beginning when he was only 23 years old , he made three discoveries: calculus, the law of universal gravity, and the spectrum of light. Although the fields of math and science are what he is best known for, most of his time was spent unsuccessfully researching chemistry and alchemy. He discovered no major advances in chemistry, and alchemy was also a failure for obvious reasons to modern scientists. The fact that he devoted so little time to physics and mathematics relative to his main projects of chemistry and alchemy makes him much more impressive. While the three aforementioned discoveries are mainly attributed to him,
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He also described integral calculus in a summation form through a variation of the trapezoidal rule in numerical analysis. This method uses the point on a curve at a specific point x0 and a point on a curve x1. By using these two points, one can create a trapezoid; the area of that trapezoid can be approximated as the area under the curve of the function. While generally not accurate where x0 and x1 are far distances apart, it becomes highly accurate as the distance becomes infinitesimally small. These examples illustrate Newton’s use of geometric principles in integral
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At the time when Newton was finished developing the method, Leibniz was only 20 years old and had not even started his endeavors in mathematics. Unfortunately, Newton, while explaining the geometric form of calculus in Principia, did not explain the “fluxions” or “fluents” in detail until 1704. This left an opportunity for Leibniz to develop and publish his own method before Newton was able to get his information out to the world. Most historians today claim that they both invented it independently even though substantial evidence suggests Newton arrived at the solution first. However, Newton cannot be known as the sole contributor by today’s standards. Due to his hesitancy to distribute his work to the public, it was not able to catch on for use. Leibniz used “dx” to denote a derivative, “f(x)” to denote a function in terms of the variable x, and a ∫ to denote an integral, the notation that is in use today. The credit for all symbols and terms in calculus belongs solely to Leibniz. It has been said that he spent days creating the “correct” symbol or notation. This precision and dedication cannot be found in Newton’s