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
The Basics A jet engine can be divided into several distinct sections: intake, compressor, diffuser, combustion chamber, turbine, and exhaust. These sections are much like the different cycles in a four-stroke reciprocating engine: intake, compression, power and exhaust. In a four-stroke engine a fuel/air mixture is is brought into the engine (intake), compressed (compression), and finally ignited and pushed out the exhaust (power and exhaust). In it's most basic form, a jet engine works in
formed many of the beliefs and practices that would guide the rest of his life and our nation, first, as the Secretary of the Treasury, and, later, as President of the United States of America. Hamilton’s early life can be divided into three main sections: his childhood, his education, and his public service. Hamilton was the son of a respectable French woman, Rachel Faucett, and a Scottish nobleman, James Hamilton. Alexander’s parents separated when he was two. His mother took custody of himself
Jazz Showcase The concert I attended was the Jazz Showcase in Rudder Theatre on Monday June21, 2004 at 7:30 p.m. Surroundings Rudder Theatre is a large venue for this Jazz Showcase. There are five sections with fifteen rows deep in each section. The theatre is decorated modestly with solid colors and nothing too spectacular or eye catching. The chairs were covered in a yellowish fabric. The initial backdrop behind the stage was a white backdrop with red and blue lighting. This backdrop would change
be triplets because the song seemed to swing and the other subdivisions didn’t match. The correct sequence and lengths of the sections in this particular song can be best labeled as I8+8 A8 B8 C6 B8 Solo8 B8 C6 D8+8 A8 B8 Solo8 Solo8. The labels A and B are to distinguish the two different verses, the label C stands for the chorus and the label D symbolized the new section (the bridge). The vocals within this song have a deeper and a more wailing kind of voice than that of the band Erasure. The song
nationalities such as the Poles and Italians (though they had always strived for a unified Italy) by giving them a favoured position in the empire, in which their nobility and relative autonomy was sustained. I will split this answer up into two sections; the Cisleithanian (Austrian) and the Hungarian parts of the empire. Both dealt with the nationalities within their borders differently and consequently were faced with varied political parties representing the demands of their group. The Habsburg