Ellipse

The story of Hypatia is what led her to her upcoming and how she made an impact to society. Her father Theon of Alexandria, Plato, Aristotle, and Plotinus influenced her in like and learning to love and have a passion for mathematics and everything that came with it. In her time of A.D she was the only woman who made a big difference. Hypatia was a popular teacher of interesting topics. She drew attention to herself by being phenomenal at what she did. Her words embraced others as much as herself by dedicating her life and virginity.She was a dedicated woman that loved at what she did and learned in her time she is an ancient woman of Alexandria that made a difference to our society of where Parabolas, hyperbolas and ellipses. Hypatia life just began let's see how it ends. She was an ancient woman in our society that made a difference is what we know and how we know it. Hypatia created things that we use to this day, she made history that…

conducted by using the formulas of x-y=a and x^2-y^2=(x-y) +b, which were referred to as simultaneous pairs. Most of her well known contributions to math were revisions to the work of her male cohorts. Three of her heavily appraised corrections and commentaries were to that of: Ptolemy’s “Almagest”, Apollonius’ review of Conics, and her father Theon’s lessons of the “Euclid Elements”. She even revised her commentary of “The Arithmetica” conducted by Diophantus. Out of all her revisions, her…

With the help of Tycho Brahe's observations, Kepler discovered that the orbits of the planets can be described with a curve. By trial and error, he discovered that an ellipse with the sun could accurately describe the path of a planet about the sun. Ellipses (which does not look like the usual circle, but as an egg) is described mainly by the length of its two axes. A circle has the same diameter if we measure it across or up and down. However, an ellipse has diameters of different lengths. The…

Greek mathematician-Apollonius of Perga On the early ages there were a group of people who questioned everything and wanted to find the reason for why it happened. Therefore this group of individuals created new solutions to find the answers to their questions and pass it on to the new generations. One of this individual was Apollonius of Perga who was known as one of the greatest Greek geometer and an astronomer.Apollonius was born in Perga in 262B.C.-190B.C. With all of his acknowledge…

gravitational pull has no influence either. The only object that exerts a substantial force of gravitational attraction with the spacecraft is the Sun. Because of this it is called the 2 Body Problem. It can be demonstrated using Newton’s Law of Gravitation that the orbit in a 2 Body Problem is a conic. What could be asked now is, what is the shape of the planets orbit? Kepler in its first law states that the orbit of the planets around the sun is an elliptical shape, with the centre of the…

The three stages are the three orbits that a satellite or spacecraft must go through: The initial circular orbit, the elliptical Hohmann Transfer orbit, and the final circular orbit. The elliptical orbit is incidentally what results in a change in velocity of the spacecraft, because the elliptical transfer orbit is closer to the Sun at the end with Earth’s than it is at the end with the Mars orbit - it will have a larger velocity near Earth than it will near Mars. The end of the ellipse closest…

statements that described the motion of planets in a sun-centered solar system. Kepler's efforts to explain the underlying reasons for such motions are no longer accepted; nonetheless, the actual laws themselves are still considered an accurate description of the motion of any planet and any satellite. Kepler's three laws of planetary motion can be described as follows: Kepler's first law - sometimes referred to as the law of ellipses - explains that planets are orbiting the sun in a path…

Degenerate Cases of Conic Sections: Conics are formed when a plane and a double cone intersect. These intersections can form a variety of conics. These include: circles, parabolas, ellipses and hyperbolas. A circle can be formed from a cone if a plane intersects with the cone at an angle perpendicular to the base of the cone. This circle is also formed by the equation: (x-h)2+ (y-k)2=r2. This equation creates a relation because the collection of points does not pass the vertical line test. To…

retired detective, Scottie, follows his old friend’s wife, Madeleine, because of her bizarre behavior after his old friend’s request in the movie Vertigo directed by Alfred Hitchcock. Scottie’s mental health starts to break down after he searches the problem with Madeleine. Vertigo is one of the most complex movies in terms of components of narration, which are plot, the three-part dramatic structure as well as narration’s range of story information. At first glance, Vertigo does not seem to…

Hence the equation of the orbit can be written as (Equation 5a). r=p/(1+e cos⁡〖(∝-∝_o 〗)) (1.11b) where p = A^2/β (1.11c) and e=A^2/β B = p B (1.11d) Equation (1.11d) is the polar equation of a conic section with ρ as the latur-rectum and e the eccentricity, with M as the focus, and the orbit of m being: (i) a circle with radius p for e=0 (ii) an ellipse for e<1 (iii) a parabola for e=1 (iv) a hyperbola for e>1 The cases of circular (e = 0) and…