# Essay about Conic Sections in Taxicab Geometry

Length: 1769 words (5.1 double-spaced pages)

Rating: Powerful Essays

#### Essay Preview

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 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.

DEFINING THE PROBLEM

Problem given by teacher was:
A probe on the surface of planet Mars has a limited amount of fuel left. Because of broken rudder it can only move north- south and east- west. Which points can it reach if it must return back to its base?
I solved the problem hence finding a shape of a circle in so-called taxicab geometry.

My research question was:
How would other conic sections look like in taxicab geometry?

INTRODUCING TAXICAB AND EUCLIDEAN DISTANCE

I think it is my duty to define the two distances that the essay is going to talk about: Euclidian and taxicab distance, as many people as well as I, probably have never heard about the taxicab distance.

EUCLIDEAN DISTANCE

Euclidean distance was proposed by Greek mathematician Euclid of Alexandria. In mathematics, the Euclidean distance or Euclidean metric is the distance between two points, which is shown as a length of a line segment and is given by the Pythagorean theorem. The formula of Euclidean distance is a squ...

... middle of paper ...

... (2014) Feature Column from the AMS. [online] Available from: http://www.ams.org/samplings/feature-column/fcarc-taxi [Accessed: 02/03/14].
P. Thompson, K. (2010) Taxicab Geometry - General Info. [online] Available from: http://www.taxicabgeometry.net/general/index.html [Accessed 02/ 03/14].
RAKANOVIČ, A. and ŠURC, D. and MITROVIČ, B. (2007) Stožnice v taksi razdalji.
WIKIPEDIA. (2014) Conic section. [online] Available from: http://en.wikipedia.org/wiki/Conic_section. [Accessed 02/03/14].
COMPONENT, C. (2007) Taxicab Geometry: Not the Shortest Ride Across Town. Iowa: Iowa State University.
BUCHANAN, L. Et al. (2012) Mathematics Standard Level. Oxford: Oxford University

Image:
PBROKS13 (2009) The three conic sections that are created when a double cone is intersected with a plane. [image] Available from: http://en.wikipedia.org/wiki/File:Conic_sections_with_plane.svg

## Need Writing Help?

Get feedback on grammar, clarity, concision and logic instantly.

## Conic Sections Essay

- 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 each separate curve, and many uses for them to be applied to as well....   [tags: Papers]

Powerful Essays
2477 words (7.1 pages)

## Questioning Strategies to Improve Understanding of Conic Sections in Math Class

- ... Data was collected in order to analyze the use of questioning strategies in a whole class setting, and how these strategies improve student understanding of conic sections. This class was video-taped on both days of a two-day teach. A portion of the video transcript for the first day showing the interaction between the students and the teacher during the second explore was the first data analyzed. During this section, the teacher was guiding the students to discover the equation for a circle....   [tags: teaching techniques]

Powerful Essays
2253 words (6.4 pages)

## Four Geometry Formulas Essay

- As you begin the course of geometry students are generally familiarized with frequently used formulas in mathematics. These formulas include finding the perimeter and area of two-dimensional figures and finding the volume and surface area of three-dimensional figures. For every diverse shape there is a related formula for finding its perimeter, area, volume, or surface area. Therefore, we will only focus on four formulas for four singular shapes or figures. We will find the perimeter of a square, the area of a triangle, the volume of a right circular cylinder and the total surface area of a sphere....   [tags: Geometry]

Powerful Essays
649 words (1.9 pages)

## The Importance of Geometry in the Construction Industry Essay

- According to J. Dee, (1608), an English scholar, “There is nothing which so much beautifies and adorns the soul and mind of man as does knowledge of the good arts and sciences. ... Many ... arts there are which beautify the mind of man; but of all none do more garnish and beautify it than those arts which are called mathematical, unto the knowledge of which no man can attain, without perfect knowledge and instruction of the principles, grounds, and Elements of Geometry.” Geometry was derived from the Greek word meaning earth measurement which focuses on the study of shapes, sizes, relative configuration, and spatial properties....   [tags: geometry, construction, topography]

Powerful Essays
1227 words (3.5 pages)

## Market Failure of the Taxicab Industry Essays

- I. Overview of the taxicab industry The Taxicab industry plays a vital and large role in the U.S. urban transportation system, employing 233,000 drivers (United States Bureau of Labor Statistics) and providing transportation to millions of Americans each day. Taxicabs differ most substantially from alternative urban transportation systems, like busses and subways, as customers select the final destination, opposed to adhering to a predefined route. This flexibility is reflected in the higher price of taxicabs (Moore and Balaker) compared to other public transit services....   [tags: business analysis and strategy]

Powerful Essays
1831 words (5.2 pages)

## Market Failure of the Taxicab Industry Essays

- When San Diego increased the number of licensed cabs by 50% in 1984, average wait time for radio-dispatched taxis fell 20% from 10 minutes to 8 minutes and average wait time at major taxi stands became negligible (Frankena and Pautler). In other cities where deregulation occurred, average wait time decreased, but fares rose, which decreased demand, thus wait time. • Higher prices: In a monopolistic situation it can be expected that the fares for taxis would be unreasonably high. To combat this, cities regulate fares, as noted above, by setting a standard fare or setting a fare ceiling....   [tags: business analysis and strategy]

Powerful Essays
1883 words (5.4 pages)

## A Direct Correlation Between The Geometry And The Activities Essay

- In this essay, I explored how a building has a direct correlation between the geometry and the activities contains. After looking at many libraries I chose to analyze the Joe and Rika Mansueto Library, University of Chicago Illinois. In order to understand a library, you first need to know a brief history. In 1731, the first Library was opened by Benjamin Franklin and his Junti Society. More than a century and a half passed by and in 1887, Melvin Dewey founded a school for librarians to get their knowledge....   [tags: Library, Public library, Librarian, Room]

Powerful Essays
941 words (2.7 pages)

## Differences in Geometry Essay

- Differences in Geometry Geometry is the branch of mathematics that deals with the properties of space. Geometry is classified between two separate branches, Euclidean and Non-Euclidean Geometry. Being based off different postulates, theorems, and proofs, Euclidean Geometry deals mostly with two-dimensional figures, while Demonstrative, Analytic, Descriptive, Conic, Spherical, Hyperbolic, are Non-Euclidean, dealing with figures containing more than two-dimensions. The main difference between Euclidean, and Non-Euclidean Geometry is the assumption of how many lines are parallel to another....   [tags: Papers]

Powerful Essays
1389 words (4 pages)

## Geometry Essay

- Geometry Geometry was actually first used in ancient Egypt and Babylon at around 2000 BC in both cases. In order for the Egyptians to build such massive structures as the pyramids they had to have made plans for them prior to the actually building, in these plans geometry had to be used. On ancient Babylonian tablets there is evidence that they understood the Pythagorean theorem. The so-called "father" of Geometry is Euclid a Greek mathematician. He wrote The Elements, books of postulates and theorems, which paved the way for modern Geometry....   [tags: Papers]

Free Essays
362 words (1 pages)

## Abstract Geometry Essay

- Abstract Geometry The ancient Egyptians and Babylonians discovered abstract Geometry. They developed these ideas that were used to build pyramids and help with reestablishing land boundaries. While, the Babylonians used abstract geometry for measuring, construction buildings, and surveying. Abstract geometry uses postulates, rules, definitions and propositions before and up to the time of the Euclid. Abstract geometry is deductive reasoning and axiomatic organization. Deductive reasoning deals with statements that have already been accepted....   [tags: Free Essays]

Free Essays
402 words (1.1 pages)