IndexIntroductionNewton's law of gravityNewton's theory of calculusWork with prisms and lightConclusionIntroductionIsaac Newton, born on 25 December 1642 in Lincolnshire, was an English mathematician, astronomer and physicist . Newton's father was a wealthy farmer who died three months before his birth. Newton's mother remarried when he was three, leaving him with his grandmother to care for him. At the age of fourteen Newton's mother decided that he should be a farmer, this interrupted his education. Newton obeyed his mother's wishes until an uncle of his convinced Newton that it was time for him to return to school. Without this uncle's advice, Newton may never have had the courage to go against his mother's wishes to return to school, without his education his legacy may not have been the same, and he may not have had the opportunities he had. When he returned to school, Newton attended Trinity College, Cambridge University where his uncle had graduated. Newton's early years at university consisted of waiting tables and taking care of the rooms of the wealthier students. In his first three years of college he took the required standard courses, but his mind was more interested in the advanced sciences. Newton spent his free time trying to teach himself as much as possible about the sciences since he didn't learn them in his lectures. His performance in class wasn't the best, but that was to be expected as he was more interested and focused on the curriculum he was learning outside of his classes. The bubonic plague arrived in Europe in 1665, this forced the university to send its students home, this closure of the university lasted two years. During his time on the farm, this is where Newton excelled by being able to focus on the things he wanted to learn and pursue. These years are known as Newton's annus mirabilis, the phrase simply meaning "a notable or notable year" (Merriam-Webster). Newton's annus mirabilis was no exaggeration; most of Newton's work dates from this period, including his theory of gravity, laying the foundations of calculus, and his work with the prism. Say no to plagiarism. Get a tailor-made essay on "Why Violent Video Games Shouldn't Be Banned"? Get an Original Essay Newton's Law of Gravity Newton's Law of Gravity doesn't show anything new about Newton that we didn't already know, but the way he went about finding out is shocking. Legend has it that Newton was sitting next to an apple tree at home in Lincolnshire where he saw an apple fall from a tree. This apple made Newton start to think about why things always fall downwards and never in another direction. He thought that the force of gravity could expand beyond the Earth. Being so intrigued, Newton immediately began trying to understand why this was always the case. Newton assumed that there was a force between all objects that did not require contact acting at a distance (Dr. Stern 2016). Knowing that there is the same force that causes the apple to fall to the ground and the movement of the Moon around the Earth, he would be able to use things he already knew. Newton began by discovering that the Moon has an acceleration that is 1/3,600 times smaller than the square of the Earth's radius (Faller 2019). Calculate the circular orbital motion of radius (R) and period (T) requiring an inward acceleration (A) which should be equal to the product of 4(pi)^2. This gave him the formula A=(4pi^2R)/(T^2). Newton next used the facts he knew about the Moon's orbit around the Earth to find the Moon's daily inward acceleration, (1/60)^2 of the acceleration relative to an objectthat falls to Earth. In his theory, he was realizing that every particle gravitationally attracts every other particle. Newton linked it to the two accelerations, that of the Moon and that of an object falling to the Earth. Newton was learning that gravitational force had to depend on mass. Newton knew that an object with mass subjected to a force had an acceleration = F/M, Galileo's idea that all objects fell to the Earth at the same speed must be constant (Faller 2019). Newton formulated the force formula: F=(G(M1)(M2))/R; G represents the universal constant of gravitational force, M1 and M2 represent the masses of two objects, and R is the radius of the distance between the two objects (Faller 2019). In simpler terms, Newton's law of gravitation states that the downward acceleration of an object toward the surface is equal to the product of the universal gravitational force and the mass of the Earth divided by the radius of the Earth. Newton may not have discovered all this during his stay home from Cambridge during the plague years, but this is where he was given the idea to pursue this goal. Since the idea came to him at home, away from school during the plague, it can be said that without the plague Newton perhaps would never have carried out this discovery, attributing to his annus mirabilis the merit of not being an exaggeration and to the original provenance of this work. Newton's Theory of CalculusDuring the plague years, Newton famously constructed his theory of calculus. It's a very debatable topic for many as to who truly invented calculus, the debate boils down to Newton and Leibniz, depending on what you consider "inventing" will give many people different opinions. His theory was motivated by other great thinkers who came before him. Newton started from the problem that the slopes of curves varied constantly and it was very difficult to provide the slope at every point on the curve. Newton was able to invent the derivative function, f'(x), this derivative function was able to give the slope at any point on the curve (Mastin 2020). Newton called this method the method of fluxions because he called the rate of change at a given point on a curve flux. Newton not only achieved differentiation but also integration. He called integration the “fluent method” (Mastin 2020). In Newton's fundamental theorem of calculus, he states that differentiation and integration are the inverses of each other. He proved that they were inverses by showing that if you take the derivative of a function and then integral you will end up with the original function you started with; this can also be done in reverse order and it will still work. Newton used integrals to find the area under a curve, the area between the curve and the x-axis. The general formula for integrating a generic function is f(x)=x^y is (x^(y+1))/(y+1). The formula gets more complicated the more difficult function you are looking at, but nevertheless Isaac Newton was able to prove that the area under the curve can be obtained using integrals. Newton did not immediately publish his work on calculus. This is where the question of who really invented calculus comes into play because Newton did not publish his work on this topic until 1693 but Leibniz published his nine years earlier (Mastin 2020). Just because Newton may not have published first doesn't mean he wasn't the first to invent calculus. Newton didn't publish his work right away because he was worried that he would be criticized for his ideas that had never been talked about before, he thought that people would think that his ideas were unconventional. Newton kept his work to himself and talked about it.