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.
At the time of trial, Mr. Wardlow tried to suppress the handgun as evidence due to the fact that he believed the gun had been seized under an unlawful stop and frisk that violated his Fourth Amendment rights. The Fourth Amendment of the United States Constitution protects the right of the people against unreasonable searches and seizures by requiring a showing of probable cause in order to obtain a warrant before conducting such searches. “In a trial motion to suppress the gun, Wardlow claimed that in order to stop an individual, short of actually arresting the person, police first had to point to ‘specific reasonable inferences’ why the stop was necessary.”(Oyez, 2000) Recognizing that an investigati...
Dante experiences a vision, at the age of 35, after experiencing traumatic events in his hometown of Florence. The events that are occurring in Florence at the time are associated with papal corruption and cause Dante to be forced into exile. Following the vision, which confirms to Dante that he has strayed from the right path in life, Dante begins his travel through the three realms, which contain the possible consequences following a person’s death. Dante’s journey begins on Good Friday, when he is escorted to the gates of Hell, moves to Purgatory and ends in Heaven. However, an escort accompanies him for duration of his journey. Virgil, who Dante has long admired, escorts Dante through Hell and...
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.
Newton’s inventive years with mathematics were from 1664 to 1696. Even though his companions also had likely various elements of the calculus, Newton summed everything up and included these ideas of his while developing new and more exact methods. The necessary elements of his thought were on hand in three tracts, De analysi (On Analysis), which went unpublished until 1711. In 1671, Newton developed a more absolute account of his course of infinitesimals, which appeared nine years after his death as “Methodus fluxionum et serierum infinitarum”.
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.
It is no mystery that without the Ancient Greeks, math as we know it today would not be the same. It is mind blowing to think that people who had no access to our current technology and resources are the ones who came up with the basic principles of the mathematics that we learn and use today without any preceding information on the topic. One of the best examples of such a person is Archimedes. Not only did he excel as a physicist, inventor, engineer, and astronomer, but he is still known today as one of the greatest mathematicians of all time. His contributions to the field laid out many of the basics for what we learn today and his brilliance shocked many. Long after his time, mathematicians were still stumped as to how he reached the genius conclusions that he did. Nicknamed “The Wise One,” Archimedes is a person who can never be forgotten.
Hurricanes get their start over the warm tropical waters of the North Atlantic Ocean near the equator. Most hurricanes appear in late summer or early fall, when sea temperatures are at their highest. The warm waters heats the air above it, and the updrafts of warm, moist air begin to rise. Day after day the fluffy cumuli form atop the updrafts. But the cloud tops rarely rise higher than about 6,000 feet. At that height in the tropics, there is usually a layer of warm, dry air that acts like an invisible ceiling or lid. Once in a while, something happens in the upper air that destroys this lid. Scientist don not know how this happens. But when it does, it's the first step in the birth of a hurricane. With the lid off, the warm, moist air rises higher and higher. Heat energy, released as the water vapor in the air condenses. As it condenses it drives the upper drafts to heights of 50,000 to 60,000 feet. The cumuli become towering thunderheads. From outside the storm area, air moves in over the sea surface to replace the air soaring upwards in the
“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.
The Bernoulli family had eight significant and important mathematicians, starting with Jacob Bernoulli, born in 1654. Though there was a great deal of hatred and jealousy between the Bernuollis, they made many remarkable contributions in mathematics and science and helped progress mathematics to become what it is today. For example, Daniel discovered a way to measure blood pressure that was used for 170 years, which advanced the medical field. Daniel’s way of measuring pressure is still used today to measure the air speed of a plane. Without the Bernoulli family’s contributions and advancements to calculus, probability, and other areas of mathematics and science, mathematics would not be where it is now.
Hurricanes are gigantic, swirling, tropical storms that are created with a wind speed over 160 miles (257 kilometers) per hour. It gives off more than 2.4 trillion gallons (9 trillion liters) of rain each day. Hurricane forms in the Southern Atlantic Ocean, Caribbean Sea, Golf of Mexico, and in the Eastern Pacific Ocean. According to www.weatherwizkids.com , a hurricane usually lasts for a week. Hurricane mostly occurs at mid-August to late October and occurs about five to six times a year. A hurricane begins at a tropical disturbance in warm ocean water with a temperature of at least 80 degrees Fahrenheit (26.5 degrees Celsius). The center of a hurricane is call the “Eye of the Hurricane” and is about 20-30 miles wide (32-48 kilometer wide). The eye is the calmest part of a hurricane and surrounding the eye is something call the “Eye Wall". When a hurricane makes a...
Analytic geometry combines algebra and geometry in a way that allows for the visualization of algebraic functions. Rene Descartes, a French philosopher, and Pierre de Fermat, a French lawyer, independently founded analytic geometry in the early 1600s. Analytic geometry subsequently paved the way for calculus and physics.
Historically speaking, ancient inventors of Greek origin, mathematicians such as Archimedes of Syracuse, and Antiphon the Sophist, were the first to discover the basic elements that translated into what we now understand and have formed into the mathematical branch called calculus. Archimedes used infinite sequences of triangular areas to calculate the area of a parabolic segment, as an example of summation of an infinite series. He also used the Method of Exhaustion, invented by Antiphon, to approximate the area of a circle, as an example of early integration.
Hurricane, name applied to migratory tropical cyclones that originate over oceans in certain regions near the equator, and particularly to those arising in the West Indian region, including the Caribbean Sea and the Gulf of Mexico. Hurricane-type cyclones in the western Pacific are known as typhoons. Hurricanes are high winds that move in a circular motion, around an eye (a low pressure center of a storm). The diameter of the area affected by winds of destructive force may exceed 150 mi. Gale winds prevail over a larger area, averaging 300 mi in diameter. The strength of a hurricane is rated from 1 to 5. Obviously 1 is the lowest and 5 is the highest strength. Hurricanes sometimes produce over 250 mm (10 in) of rain and lead to extensive flooding. Which in turn can cause another problem in its self.
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...
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...