sqrt2.tex -...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
\documentclass[12pt]{article} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsthm} \usepackage[letterpaper, margin=1 in]{geometry} \usepackage{graphicx} \usepackage{hyperref} \usepackage{plain} \usepackage{amsrefs} \title{The Irrationality of $ \sqrt{2} $} \author{Paul Glaze} \date{\today} \begin{document} \maketitle %\section{Introduction}\label{firstsection} % % % %There are many different representations of numbers in mathematics. Few are as important as irrational numbers. Calling them irrational numbers is probably the second worst name for a numbering system, next to imaginary. Irrational numbers are somewhat counter intuitive at times because they can not be represented as a fraction. Irrational number have been around for a very long time it was a Pythagorean named Hippasus who first proved them \cite{Wikipedia}. It has been said that people reacted quite violently to his assertion of a numbers. But thanks to this proof it opened the door to many advancements in mathematics. Before for this point number were thought to be integers or ratios of integers. % %In the first part of the paper we ill discuss how Hippasus came across irrational numbers \cite{Fritz}. At the same time why irrational numbers are needed, particularly because they are impassible to represent as a ratio if only using integers. They do not terminate when represented as a decimal. In the next section of he paper we will expand on the use of irrational numbers and how they have been used to prove other mathematical structures. This paper will finished by showing that the $ \sqrt{2} $ is no more irrational than any other number \cite{Agafonov}. It is just miss understood.
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern