Hyperbola

problems, which seemed interesting to explore. I started with a basic example, just to compare Euclidean and taxicab distance and after that I went further into the world of taxicab geometry. I explored the conic sections (circle, ellipse, parabola and hyperbola) of taxicab geometry. All pictures, except figure 12, were drawn by me in the program called Geogebra.

As the title suggests, Apollonius’ Conics deals with the various conic sections, shapes that arise when one cuts the cone in different ways. However, we leave the cone rather quickly in our foray into the conic sections, exploring the parabola, hyperbola, circle, and ellipse as they exist outside the cone and the various line relationships that comprise them. After we find the diameter for these sections, the cone makes a sudden reappearance as we construct the conic sections from given lines and

the ratio is less than 1, for a parabola the ratio is 1, and for a hyperbola the ratio is greater than 1. These ratios are known as the eccentricity, so we can say that any conic section is all points whose distance to the focus is equal to the eccentricity times the distance to the directrix. A circle has an eccentricity of zero, an ellipse has an eccentricity between 0 and 1, a parabola has an eccentricity of 1, and a hyperbola has an eccentricity greater than 1. Ellipse is known by

sight. What connects these different areas is called Conic Sections. Where do they come from? Conic Sections are figures formed by the intersection of a plane and a right circular cone. A conic section may be a circle, an ellipse, a parabola, or a hyperbola . They were first discovered by a Greek mathematician, Menaechmus. He wanted to come up with a model that showed all three different conic sections. With the help of Appollonius, they came up with the “Double Napped Cone”, which clearly shows all

Pool Pockets For this problem we have a modified pool table that only has four pockets, one in each corner. The ball leaves the bottom left corner at a forty five degree angle and rebounds off the wall at a forty five degree angle until it lands in a pocket (corner). We have to collect data containing the dimensions of the table we used, the number of rebounds it took for the ball to land in a pocket, and which pocket it will land in. We will use this data to find patterns and attempt to find a

Mr. Diaz 10 Algebra 2 5 June 2016 Parabola vs. Hyperbola Essay A parabola and a hyperbola are two of the same, but also are very different. The definition of a conic section is a section (or slice) through a cone. By taking different slices through a cone you can create a parabola or a hyperbola. Each has its own place independently, but some things function very similar to one another. But the graph you will get whether it be a parabola or a hyperbola, will always be relatively similar. In a parabola

I. Introduction Time is always an interesting topic for people during different period. What is time? It is the thing that is measured as seconds, minutes, hours, days, years, etc. From Mayan to modern scientists like Einstein, they all tried to study and find the way to determine an exactly time. Nowadays, if people want to know what time is it, they only need to raise head and have a look at clock on the wall. In addition, to ensure a global society with order, people even found a way to measure

Pool Pockets For this problem we were given a modified pool table, in which there are only corner pockets, no side pockets. We imagine there is a ball starting in the bottom left corner and shooting at a 45 degree angle and bouncing off the side of the table until it rolls into a hole. The question that I am trying to answer however is if I can predict how many times the ball will hit a wall before landing in a pocket and also which pocket it will land in. During this problem a learned many different

A hyperbola was added in and after some tinkering with the position of hyperbola AD-AN, it created another segment of the mouth, thus creating an open mouth (figure 25). On the original sketch many of the circles had domains set to them, however when using geogebra it created great difficulty

Introduction Mobile positioning technology has become an important area of research, for emergency as well as for commercial services. Mobile positioning in cellular networks will provide several services such as, locating stolen mobiles, emergency calls, different billing tariffs depending on where the call is originated, and methods to predict the user movement inside a region The simple method for mobile telephone tracking and positioning with high accuracy which presents the location of a