#### Date of Award

8-1969

#### Document Type

Thesis

#### Degree Name

Master of Science

#### Degree Discipline

Mathematics

#### Abstract

The intent of this project is to prove some of the commonly used Algebraic Properties regarding reflections, translations, and rigid rotations and to extend these concepts to three dimensions. The approach considered will be in terms of point sets.

DEFINITIONS

Relation:

The statement that R is a relation means that R is a subset of the cartesian product A X B.

Cartesian Product:

The set of all ordered pairs whose list numbers are m©fflbers of a given set A and whose second number is a member of a given set B.

Function:

A relation where X and Y are related such that for each Y number there is a unique X number in the set.

Example X=Y

An ordered Pair:

Is two numbers having the form (X, Y) such that X is the first number and Y is the second number.

Example (3,6)

An ordered Triple:

Is three numbers having the form (X, Y, Z) where X is the first number, Y the second number, and Z the third number.

Example: (2,4, -1).

#### Committee Chair/Advisor

A. D. Stewart

#### Committee Member

Samuel E. Good

#### Committee Member

Whitmore

#### Publisher

Prairie View Agriculture And Mechanical College

#### Rights

© 2021 Prairie View A & M UniversityThis work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

#### Date of Digitization

4/6/2022

#### Contributing Institution

John B Coleman Library

#### City of Publication

Prairie View

#### MIME Type

Application/PDF

#### Recommended Citation

Davis, D. A. (1969). Reflections, Translations And Rotations Of Point Sets In E2 And E3. Retrieved from https://digitalcommons.pvamu.edu/pvamu-theses/1449