Ever wonder how scientists figure out how long it takes for the radiation from a nuclear weapon to decay? This dilemma can be solved by calculus, which helps determine the rate of decay of the radioactive material. Calculus can aid people in many everyday situations, such as deciding how much fencing is needed to encompass a designated area. Finding how gravity affects certain objects is how calculus aids people who study Physics. Mechanics find calculus useful to determine rates of flow of fluids in a car. Numerous developments in mathematics by Ancient Greeks to Europeans led to the discovery of integral calculus, which is still expanding. The first mathematicians came from Egypt, where they discovered the rule for the volume of a pyramid and approximation of the area of a circle. Later, Greeks made tremendous discoveries. Archimedes extended the method of inscribed and circumscribed figures by means of heuristic, which are rules that are specific to a given problem and can therefore help guide the search. These arguments involved parallel slices of figures and the laws of the lever, the idea of a surface as made up of lines. Finding areas and volumes of figures by using conic section (a circle, point, hyperbola, etc.) and weighing infinitely thin slices of figures, an idea used in integral calculus today was also a discovery of Archimedes. One of Archimedes's major crucial discoveries for integral calculus was a limit that allows the "slices" of a figure to be infinitely thin. Another Greek, Euclid, developed ideas supporting the theory of calculus, but the logic basis was not sustained since infinity and continuity weren't established yet (Boyer 47). His one mistake in finding a definite integral was that it is not found by the sums of an infinite number of points, lines, or surfaces but by the limit of an infinite sequence (Boyer 47). These early discoveries aided Newton and Leibniz in the development of calculus. In the 17th century, people from all over Europe made numerous mathematics discoveries in the integral calculus field. Johannes Kepler "anticipat(ed) results found… in the integral calculus" (Boyer 109) with his summations. For instance, in his Astronomia nova, he formed a summation similar to integral calculus dealing with sine and cosine. F. B. Cavalieri expanded on Johannes Kepler's work on measuring volumes. Also, he "investigate[d] areas under the curve" ("Calculus (mathematics)") with what he called "indivisible magnitudes.
Officer Wheetley stated that he only had records of Aldo’s successes and no records of the times when he didn’t succeed. With no evidence of Aldo’s bad performances, the Supreme Court concluded that “ when a dog alerts, the fact that the dog has been trained and certified is simply not enough to establish probable cause.” Also, the Supreme Court established requirements that a dog and handler would have to meet to support a finding of “probable
The Court held that because of the “special facts” the “attempt to secure evidence of blood-alcohol content in this case was an appropriate incident to petitioner’s arrest.” Under current jurisprudence, we would construe the language about “special facts” as relating to the exigent circumstances exception to the Fourth Amendment – which resists categorical rules – and instead focuses on the need for the intrusion and the availability of a warrant. However, the language also justifies the search as “incident to petitioner’s arrest,” which would indicate that the test was upheld as a search incident-to-arrest. In situations where it is appropriate, that has been described as a “categorical” exception to the warrant requirement that does not require any case-by-case
There has been a large variety of horror films produced throughout the last fifty years. People are always going to be frightened and scared by different types of horror films. But, what type of horror film scares more people, and were men or women more frightened by these horror films? Each one of the horror films had its own agenda to frighten its audience using several different methods of horror. Some of these methods were more so directed at the female audience than the male audience. Most horror movies show the female as being vulnerable, because in real life females are defenseless against monsters.
In Dante’s Inferno, the relationship between Dante the Pilgrim and Virgil the Guide is an ever-evolving one. By analyzing the transformation of this relationship as the two sojourn through the circles of hell, one is able to learn more about the mindset of Dante the Poet. At the outset, Dante is clearly subservient to Virgil, whom he holds in high esteem for his literary genius. However, as the work progresses, Virgil facilitates Dante’s spiritual enlightenment, so that by the end, Dante has ascended to Virgil’s spiritual level and has in many respects surpassed him. In Dante’s journey with respect to Virgil, one can see man’s spiritual journey towards understanding God. While God loves man regardless of his faults, His greatest desire is to see man attain greater spirituality, in that man, already created in God’s image, may truly become divine, and in doing so, attain eternality.
Hurricanes form over the ocean. Easterly waves, what hurricanes develop from, are long, narrow regions of low pressure which occur in ocean winds called trade winds. At first, these easterly waves can grow into something called, a tropical depression. A tropical depression occurs when winds are up to 31 mph. Then tropical depressions can be upgraded into a tropical storm if the winds reach speeds of 74 mph or less. Then finally a the storm can be bumped up into a hurricane if the winds reach 75 mph.
Hurricanes are born over the warm waters of tropical oceans and are formed by a low-pressure system caused by the heating of water. The heat causes the air to rise and form lower pressures in a feedback loop, making the hurricane stronger. Heavy rain results from a condensation of water and strong winds develop from warm air rushing to the eye of the hurricane. Essentially, greater storms and winds occur when the hurricane feeds of the rising temperature of the water. In addition, researchers studied disturbances and intense thunderstorms in the atmosphere over Western Africa and believe they are partly to blame for extreme hurricanes affecting the United States and Canada. While these are all the main ingredients of a perfectly natural process, they were not the primary causes of the damage done by Hurricane
Film scholar and gender theorist Linda Williams begins her article “Film Bodies: Genre, Gender and Excess,” with an anecdote about a dispute between herself and her son, regarding what is considered “gross,” (727) in films. It is this anecdote that invites her readers to understand the motivations and implications of films that fall under the category of “body” genre, namely, horror films, melodramas, (henceforth referred to as “weepies”) and pornography. Williams explains that, in regards to excess, the constant attempts at “determining where to draw the line,” (727) has inspired her and other theorists alike to question the inspirations, motivations, and implications of these “body genre” films. After her own research and consideration, Williams explains that she believes there is “value in thinking about the form, function, and system of seemingly gratuitous excesses in these three genres,” (728) and she will attempt to prove that these films are excessive on purpose, in order to inspire a collective physical effect on the audience that cannot be experienced when watching other genres.
Modern day horror films are very different from the first horror films which date back to the late nineteenth century, but the goal of shocking the audience is still the same. Over the course of its existence, the horror industry has had to innovate new ways to keep its viewers on the edge of their seats. Horror films are frightening films created solely to ignite anxiety and panic within the viewers. Dread and alarm summon deep fears by captivating the audience with a shocking, terrifying, and unpredictable finale that leaves the viewer stunned. (Horror Films)
“Midway along the journey of our life” (Canto 1) Dante the Pilgrim says at the beginning of his journey. Through out the comedy and the Pilgrims vision of hell, I believe he was truly on a journey of self-discovery. Dante encountered a guide to help him in his journey throughout the nine circles of hell. Going deeper and deeper into hell Dante realized many different sins that he could have committed in his life and realized the things that he did not need anymore. Base on the end of his journey I believe that Dante truly found himself and found a new person within himself.
Horror movies have been part of mainstream cinema since the early 1930s when films such as Dracula and Frankenstein were created. As the horror genre evolved, so did the stories in the films. Friday the 13th (Marcus Nipsel, 2009) is a very good example of this evolution. Even though it is a remake, Friday the 13th changed the way horror movies were seen by the audience. The ideas and theory behind this slasher sub-genre of horror films can be summed up in a book. Carol Clover, an American professor of film studies, wrote a book in 1992 entitled Men, Women, and Chainsaws: Gender in the Modern Horror Film in which she described the horror film genre. In a chapter entitled “Her Body, Himself”, Clover describes how weapons play a very important role in horror movies as well as explaining her Final Girl theory. Her book’s ideas changed not only academic notions but also popular beliefs on horror films. The 2009 remake of Friday the 13th implies that Carol Clover’s ideas about 80s slasher films, including male tormentors, the importance of weapons, and the Final Girl, have stayed the same through the years.
Geometry, a cornerstone in modern civilization, also had its beginnings in Ancient Greece. Euclid, a mathematician, formed many geometric proofs and theories [Document 5]. He also came to one of the most significant discoveries of math, Pi. This number showed the ratio between the diameter and circumference of a circle.
Hurricanes originate as tropical disturbances over warm oceans with trade winds. The tropical turbances intensify into tropical depressions, and eventually into a tropical storm. They only originate in the tropical trade winds because the ocean temperatures are quite warm there. Powered from the heat that the sea gives off, they are steered by the east trade winds and the temperate west ones, as well as by their own ferocious energy. Around their core, winds grow with a tremendous amount of velocity creating violent seas. As they move toward the shore, they move the ocean inward, while spawning tornadoes and producing torrential rains and floods.
The 17th Century saw Napier, Briggs and others greatly extend the power of mathematics as a calculator science with his discovery of logarithms. Cavalieri made progress towards the calculus with his infinitesimal methods and Descartes added the power of algebraic methods to geometry. Euclid, who lived around 300 BC in Alexandria, first stated his five postulates in his book The Elements that forms the base for all of his later Abu Abd-Allah ibn Musa al’Khwarizmi, was born abo...
Leibniz had many contributions to math and science. He created his own form of Binary Arithmetic with an attempt to reduce complex ideas to there simplest forms. His binary representations are still used today in modern computers. He also created a calculating machine that he wanted to use to make an easier way to create fewer mistakes. The most important part of the machine was a geared-wheel that had numbers along its teeth that allowed multiplication by simply turning a handle; this simple piece was used in all calculators up until electronic calculators were created. Calculus was easily one of Leibniz’s most important contributions to math; his main purpose was to simplify the then complex math. He created two symbols that will forever be used in math. The ‘d’ notation for differentiation, and the other was the integral sign; used to find the areas under curves.
Differential calculus is a subfield of Calculus that focuses on derivates, which are used to describe rates of change that are not constants. The term ‘differential’ comes from the process known as differentiation, which is the process of finding the derivative of a curve. Differential calculus is a major topic covered in calculus. According to Interactive Mathematics, “We use the derivative to determine the maximum and minimum values of particular functions (e.g. cost, strength, amount of material used in a building, profit, loss, etc.).” Not only are derivatives used to determine how to maximize or minimize functions, but they are also used in determining how two related variables are changing over time in relation to each other. Eight different differential rules were established in order to assist with finding the derivative of a function. Those rules include chain rule, the differentiation of the sum and difference of equations, the constant rule, the product rule, the quotient rule, and more. In addition to these differential rules, optimization is an application of differential calculus used today to effectively help with efficiency. Also, partial differentiation and implicit differentiation are subgroups of differential calculus that allow derivatives to be taken to more challenging and difficult formulas. The mean value theorem is applied in differential calculus. This rule basically states that there is at least one tangent line that produces the same slope as the slope made by the endpoints found on a closed interval. Differential calculus began to develop due to Sir Isaac Newton’s biggest problem: navigation at sea. Shipwrecks were frequent all due to the captain being unaware of how the Earth, planets, and stars mov...