Taxicab Geometry in a High School Setting

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2016-04-01
Authors
Halverson, Alex
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Mathematics
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Honors Projects and Posters
University Honors Program

The Honors project is potentially the most valuable component of an Honors education. Typically Honors students choose to do their projects in their area of study, but some will pick a topic of interest unrelated to their major.

The Honors Program requires that the project be presented at a poster presentation event. Poster presentations are held each semester. Most students present during their senior year, but may do so earlier if their honors project has been completed.

This site presents project descriptions and selected posters for Honors projects completed since the Fall 2015 semester.

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Mathematics
Abstract

This project focuses on implementing a section studying non-Euclidean geometry into a standard high school geometry course’s textbook. Taxicab geometry fits this project very well because the only change from Euclidean geometry is the method of measuring distance. The section begins by introducing the topic of taxicab distance and how to calculate it. Then, by using the new method of measuring distance, it continues with an activity using the new geometry. Finally, the section finishes by discussing applications of taxicab geometry in the real world. Following the content is a collection of practice problems that allow students to use the methods that were discussed in the section. This material could be used at the end of a high school geometry course as an enrichment section. Additionally, it provides insight for some uses of different types of mathematics in the real world. Overall, the result of this project is a section of a textbook to implement at the end of a high school geometry course that introduces new and interesting mathematics that enrich student understanding of mathematics and its uses.

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