Conic Sections The term conic sections is used when discussing the derivation of a line that is a locus of points equal distance from either a line, a point, both a line and a point, two lines, etc. The term conic sections also can be used when discussing certain planes that are formed when they are intersected with a right circular cone. The planes, or lines as we know them, consist of the circle, the ellipse, the parabola, and the hyperbola. (West, 112) There are different ways to derive
Project #2 - Conic Sections Conic sections are the various gemetric figures created by the interection of a plane. They are among the oldest curves in history and is one of the oldest area of study for mathmaticians. conics were discovered by Menaechmus (c. 375 - 325 BC), a Greek pupil of Plato and Exodus. He was trying to solve the famous problem duplicating a cube. Euclid studied them and Appollonius reinforced and expanded previous results of conics into a book he named Conic Sections. It is a series
In this essay the conic sections in taxicab geometry will be researched. The area of mathematics used is geometry. I have chosen this topic because it seemed interesting to me. I have never heard for this topic before, but then our math teacher presented us mathematic web page and taxicab geometry was one of the topics discussed there. I looked at the topic before and it encounter problems, which seemed interesting to explore. I started with a basic example, just to compare Euclidean and taxicab
Conic sections are used all over the world. Conic sections are used in things such as bridges, roller coasters, stadiums, and other objects. A conic section is the intersection of a plane with a cone. The changes in the angle of the intersection produce a circle, ellipse, parabola, and hyperbola. All the types of conic sections can be identified using the general form equation. The general form equation is x2+Bxy+Cy2+Dx+Ey+F=0. Using the general form equation can help identify each type of conic
Introduction I chose to focus on how the use of questioning strategies in a whole class setting improves student understanding of conic sections because I struggle with using open-ended questioning. I see how “yes” and “no” questions do not usually cause students to think, since the answer to the question is often in the question. However, from my own experience as a teacher, simply asking an open-ended question about a new topic can cause frustration. If the students do not have any idea of how
Apollonius of Perga Apollonius was a great mathematician, known by his contempories as " The Great Geometer, " whose treatise Conics is one of the greatest scientific works from the ancient world. Most of his other treatise were lost, although their titles and a general indication of their contents were passed on by later writers, especially Pappus of Alexandria. As a youth Apollonius studied in Alexandria ( under the pupils of Euclid, according to Pappus ) and subsequently taught at the university
Hypatia of Alexandria Hypatia was born in 370 A.D. in Alexandria, Egypt. From that day on her life was one enriched with a passion for knowledge. Theon, Hypatia’s father whom himself was a mathematician, raised Hypatia in an environment of thought. Both of them formed a strong bond as he taught her his own knowledge and shared his passion in the search of answers to the unknown. Under her fathers discipline he developed a physical routine for her to ensure a healthy body as well as a highly functional
No other scholar has affected more fields of learning than Blaise Pascal. Born in 1623 in Clermont, France, he was born into a family of respected mathematicians. Being the childhood prodigy that he was, he came up with a theory at the age of three that was Euclid’s book on the sum of the interior of triangles. At the age of sixteen, he was brought by his father Etienne to discuss about math with the greatest minds at the time. He spent his life working with math but also came up with a plethora
Blaise Pascal was many things, a physicist, an inventor, a writer, and even a Christian philosopher, but the one thing that most remember him by is a mathematician. Pascal was a very successful man, but in order to fully understand how his success came about, one must go back to his beginning. Pascal was born in Clermont-Ferrand, France, June 19, 1623, and died August 19, 1662 in Paris, France. He was the third child, and the only child to Etienne and Antoinette Pascal. He was extremely close to
of 16, Pascal began to play an active role in “Academie Parisienne”. There, Pascal became the principal disciple of Girard Desargues, a professor working there because he was the only one who appreciated his work in geometry. Pascal began work on conics and published several papers to do with geometry. In fact, in June 1639, Pascal has already made a significant discovery with his “mystical hexagram”. In 1641, he began to suffer from problems of health that delayed his research for a year, but he
many of his geometry theorems, including his mystic hexagon. In December 1639 he and his family left Paris and moved to Rouen where his father Etienne was appointed tax collector for Upper Normandy. Soon after settling down in Rouen his Essay on Conic Sections was published in February of 1640. It was his first great work. Pascal also invented the first digital calculator to aid his father in his tax collecting duties. For three years he worked 1642 - 1545. Dubbed the Pascaline, it resembled a mechanical
Mathematical Contributions of Blaise Pascal Introduction Blaise Pascal was born on June 19, 1623 in Clermont Ferrand. His nationality was french. He died in 1662. He was credited for his imaginative and subtle work in geometry and other branches of mathematics. His work influenced later generations of theologians and philosophers, helping make mathematics what it is today. Blaise Pascal is considered part of the foundation of the very heart of mathematics.
contributed to hydraulics, including da Vinci, Mariotte and Boyle. The scientist who discovered the main principle I will be talking about is Pascal. A French scientist who studied math and physics. His work included studying atmospheric pressure, conic sections and the principles of hydrostatics. After Pascal there is Bernoilli, Franklin and Froud, who all also contributed to the science of hydraulics. How it works (the physics part) The basic rule of using hydraulic power is Pascal's Principle
Democritus. A more precise formulation of concepts led to the realisation that the rational numbers did not suffice to measure all lengths. A geometric formulation of irrational numbers arose. Studies of area led to a form of integration. The theory of conic sections show a high point in pure mathematical study by Apollonius. Further mathematical discoveries were driven by the astronomy, for example the study of trigonometry. The major Greek progress in mathematics was from 300 BC to 200 AD. After this time
Probability and Genetics Probability theory is the study of the likelihood of an occurrence of random events in order to predict future behaviors of a system (2). The principles of probability are widely used. In genetics, for example, probability is used to estimate the likelihood of gene distribution from one generation to the next. In business, insurance companies use the principles of probability to determine risk groups. Probability is closely related to statistics since uncertainty always
an addition that was completed in 1999. It has about 500 gray movie theater seats. There are three sections - the left, middle, and right. The middle section is the widest section. Most people sit there. The younger teens generally sit near the front; where as the older members tend to sit closer to the back. Some of the youth workers sit on near the back of the right section. The left section is usually empty. The carpet is gray and black. The sidewalls are brick from floor to ceiling. They
Is Hamlet Sane or Insane... Is Hamlet sane or insane that is the question. There are many sections in the play which show portray him as being insane but there are such as the when he hears of his fathers death. On the other hand Shakespeare illustrates Hamlet as a sane person when ever he is with a non guilty party. Hamlet is clearly sane though because he acknowledges that he is putting on an act whenever he is acting crazy. Hamlet is depicted as insane in many scenes during the play. One
Review of Rudy Tomedi’s No Bugles, No Drums What are the major wars in which the U.S. fought? A typical American might mention the Revolutionary War, the Civil War, World War I, World War II, Vietnam, the Gulf War, and most recently, the war in Iraq. However, one war absent from this list proved to be one of the most casualty-laden but least recognized by the American public as a significant war: the Korean War. In his book No Bugles, No Drums: An Oral History of the Korean War, Vietnam veteran
Titanic Passenger I am writing my first entry aboard this incredible vessel today, primarily because I have been spending the last three days exploring the sections open to my fellow third-class passengers and I. What I have seen is extraordinary, especially when first boarding the ship. The halls and staircases of the first class section were like nothing I had ever seen before in my life. They were blanketed in luxury from end to end. The first class passengers I had managed to see wore their
accidents that occur to cause them. Third, the responsibilities of both the employee and the supervisor when an accident occurs. There will also be sections on types of injuries that occur, and how to prevent them from happening. The Occupational Safety and Health Administration (OSHA) is discussed and the actions taken by the agency. Finally, there are sections on discrimination of injured employees, and how to manage light duty personnel. If an employee who has an accident while on the clock at work