# Isaac Newton: Annus Mirabilis

Isaac Newton, born December 25, 1642, in Lincolnshire, was an English mathematician, astronomer, and physicist. Newton’s father was a wealthy farmer who died three months before he was born. Newton’s mother remarried when he was three, leaving him with his grandmother to take care of him. At the age of fourteen, Newton’s mother decided that he should be a farmer, this halted his education. Newton obeyed his mother’s wishes until an uncle of his convinced Newton that it was time for him to go back to school. Without the advice of this uncle, Newton may have never had the courage to go against his mother’s wishes to go back to school, without his education his legacy may not be the same as he may not have had the opportunities he had. When returning to school, Newton attended the University of Cambridge Trinity College where his uncle had graduated from. Newton’s early years at the university consisted of him waiting on tables and taking care of wealthier students' rooms. During his first three years attending the university, he was taking the standard classes required but his mind was more interested in advanced sciences. Newton spent his spare time trying to teach himself as much as he could about the sciences since he was not learning about them in his classes. His performance in his classes was not the best but this could have been 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 caused the university to send its students home, this closing of the university lasted for two years. During his time back home on the farm, this is where Newton excelled being able to focus on the things he wanted to learn about and pursue. These years are known as Newton’s annus mirabilis, the phrase simply means, “a remarkable or notable year. Newton’s annus mirabilis was no exaggeration; the bulk of Newton’s work came from during this time including his theory on gravity, which laid the foundation of calculus, and his work with the prism.

Newton’s law on gravity shows nothing new about Newton that we did not already know, but the way in which he went about discovering it is shocking. Legend has it that Newton was sitting by an apple tree back home in Lincolnshire where he saw an apple fall from a tree. This apple made Newton start to think about why do things always fall straight down, never any other direction. He thought the power of gravity might expand further than Earth. Being so intrigued Newton immediately began to try to figure out why this was always the case.

Newton assumed there was a force between all objects that did not require contact acting from a distance. Knowing if the same force that made the apple fall to the ground and the motion of the moon around Earth, he would be able to use things he already knew. Newton started by discovering that the Moon has an acceleration that is 1/3,600 times smaller than the square of the radius of the Earth. Calculating the circular orbital motion of Radius (R) and period (T) requires an inward acceleration (A) that would have to be equal to the product of 4(pi)^2. This gave him the formula A=(4pi^2R)/(T^2). Next Newton used facts he knew about the Moon's orbit of Earth to find the Moon's inward acceleration per day, (1/60)^2 of the acceleration compared to a falling object on Earth. In his theory, he was realizing that every particle attracts every other particle gravitationally. Newton related this to the two accelerations, of the moon and of an object falling to the ground on Earth. Newton was learning that the gravitational force had to be dependent on mass. Newton knew an object with mass experiencing a force had an acceleration=F/M, had to be constant Galileo's idea that all objects fell to Earth at the same rate. Newton came up with the formula for force, F=(G(M1)(M2))/R; G represents the universal constant for gravitational force, M1 and M2 represent the masses of two objects, and R being the radius of the distance between the two objects. In simpler terms, Newton’s law of gravitation says that the downward acceleration of an object toward the surface is equal to the product of the universal gravitational force and the mass of Earth divided by the radius of Earth. Newton may not have discovered all of this during his time home from Cambridge during the plague years, but this is where the idea to pursue this was given to him. Since the idea came to him at home, away from school during the plague, it is able to be said that without the plague Newton may never have pursued this discovery, crediting his annus mirabilis for being no exaggeration and where this work originally came from.

During the plague years, Newton famously built his own theory for calculus. It is a very debatable topic to many about who truly invented calculus, the debate comes down to Newton and Leibniz, depending on what you consider “inventing” will give many people different opinions. His theory was motivated by fellow great thinkers that came before him. Newton started with the problem that slopes of curves constantly varied and it was very difficult to give the slope at any given point on the curve. Newton was able to come up with the derivative function, f’(x), this derivative function was able to give the slope at any given point of the curve. Newton called this method, the method of fluxions because he called the rate of change at a given point on a curve a fluxion.

Newton not only came up with differentiation but also integration. He called integration the “method of fluent”. In Newton’s fundamental theorem of calculus, he states that differentiation and integration are inverses of one another. He proved that they were inverses by showing that if you take the derivative of a function and then it's integral you will end up with the original function you started with; this can also be done in the reverse order and 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 for the more difficult of a function you are looking at, but nonetheless Isaac Newton was able to show the area under the curve can be obtained using integrals.

Newton did not post his work on calculus right away. This is where the situation of who truly invented calculus first comes into play because Newton did not publish his work on this until 1693 but Leibniz posted his nine years earlier. Just because Newton may not have published first does not mean he was not the first to invent calculus. Newton did not publish his work right away because he was worried criticized for his ideas that had never been talked about before, he thought people would think his ideas were unconventional. Newton kept his work to himself and only talked about it to his friends. Newton may not have published until 1693 but his work on calculus started way before that as he was home from Cambridge during the bubonic plague.

Newton was always very interested in many topics, one included light and colors. Newton wanted to investigate the refraction of sunlight into colors because this was not yet understood and begun to do so by cutting a small hole in his window shade to let in light. The light that came into his room was retracted by a prism and the light that came in was a variety of rainbow colors. Very interested in how this was happening he cut even more holes into his shades, this time a variety of sizes and different shapes, yet the light still turned oblong once coming through the shade no matter the size or shape of the hole. Taking his experiment even further he retracted light onto a piece of wood that had been drilled with a small hole, obtaining light of pure color. With the experiment of the wood, Newton was able to show that blue light refracted through a second prism and yielded the same blue light. This was true for other colors as well; he proved that the angle that the light was reflected on his wall was dependent on the color of the light that would be shown, the different colors of the light the different refrangibility that color had. Newton came up with the idea that the colors themselves are not revealed by the light but come from the light.

Newton once again was slow to publish his work with prisms and light, this was nothing new to Newton. He was worried about how his work would be viewed in the world. Even though his work was done in 1666 it was not published until 1672 when his New Theory of Light and Colors appeared in Philosophical Transactions of the Royal Society. Newton received backlash right away from people such as Robert Hooke, Hooke had different ideas and theories of color than those of Newton. Newton published Optics in 1702 which was once again some of his initial experiments with light that took place in his bedroom during the plague years.

Throughout Newton’s career, he was not only a well-accomplished mathematician but well accomplished in anything he was interested in. Newton had no time in his career as big as the plague years, his annus mirabilis. During this time away from Cambridge University he was able to focus on the things that interested him instead of the coursework that he may have been forced to take to complete his degree. Newton was able to prove his theory of gravity, lay the foundations of calculus, and explore the colors of light through a prism. Although not all of these works were published during his annus mirabilis, this is where they started. He may have still worked on them after this time period but none other than the idea began during the plague and that is where he started to work on those things. Most great things do not come in short periods of time such as a year or even two years, these great things take time with trial and error. Newton throughout his career was always hesitant to publish, the majority of his work was not posted right away, as he was worried about the criticism of others. There is no doubt that the bulk of Newton’s work came during these years, his annus mirabilis.

## Works Cited

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