Conics and geometry

Conics and Geometry is a report that focuses on the development of new approaches in mathematics by breaking from the accepted norm of the time. The conics themselves have their beginning in this manner. The author uses three ancient problems in geometry to illustrate this trend. Doubling the cube,...

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Bibliographic Details
Main Author: Johnson, William Isaac
Format: Others
Language:English
Published: 2011
Subjects:
Online Access:http://hdl.handle.net/2152/ETD-UT-2010-08-1565
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spelling ndltd-UTEXAS-oai-repositories.lib.utexas.edu-2152-ETD-UT-2010-08-15652015-09-20T16:56:38ZConics and geometryJohnson, William IsaacConicsGeometryTaxicabNon-EuclideanThree ancient problemsConics and Geometry is a report that focuses on the development of new approaches in mathematics by breaking from the accepted norm of the time. The conics themselves have their beginning in this manner. The author uses three ancient problems in geometry to illustrate this trend. Doubling the cube, squaring the circle, and trisecting an angle have intrigued mathematicians for centuries. The author shows various approaches at solving these three problems: Hippias’ Quadratrix to trisect an angle and square the circle, Pappus’ hyperbola to trisect an angle, and Little and Harris’ simultaneous solution to all three problems. After presenting these approaches, the focus turns to the conic sections in the non-Euclidean geometry known as Taxicab geometry.text2011-01-05T17:53:28Z2011-01-05T17:53:33Z2011-01-05T17:53:28Z2011-01-05T17:53:33Z2010-082011-01-05August 20102011-01-05T17:53:33Zthesisapplication/pdfhttp://hdl.handle.net/2152/ETD-UT-2010-08-1565eng
collection NDLTD
language English
format Others
sources NDLTD
topic Conics
Geometry
Taxicab
Non-Euclidean
Three ancient problems
spellingShingle Conics
Geometry
Taxicab
Non-Euclidean
Three ancient problems
Johnson, William Isaac
Conics and geometry
description Conics and Geometry is a report that focuses on the development of new approaches in mathematics by breaking from the accepted norm of the time. The conics themselves have their beginning in this manner. The author uses three ancient problems in geometry to illustrate this trend. Doubling the cube, squaring the circle, and trisecting an angle have intrigued mathematicians for centuries. The author shows various approaches at solving these three problems: Hippias’ Quadratrix to trisect an angle and square the circle, Pappus’ hyperbola to trisect an angle, and Little and Harris’ simultaneous solution to all three problems. After presenting these approaches, the focus turns to the conic sections in the non-Euclidean geometry known as Taxicab geometry. === text
author Johnson, William Isaac
author_facet Johnson, William Isaac
author_sort Johnson, William Isaac
title Conics and geometry
title_short Conics and geometry
title_full Conics and geometry
title_fullStr Conics and geometry
title_full_unstemmed Conics and geometry
title_sort conics and geometry
publishDate 2011
url http://hdl.handle.net/2152/ETD-UT-2010-08-1565
work_keys_str_mv AT johnsonwilliamisaac conicsandgeometry
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