@article {MATHEDUC.06560937,
author = {Matsuura, Ryota and Sword, Sarah},
title = {Illuminating coordinate geometry with algebraic symmetry.},
year = {2015},
journal = {Mathematics Teacher},
volume = {108},
number = {6},
issn = {0025-5769},
pages = {470-473},
publisher = {National Council of Teachers of Mathematics (NCTM), Reston, VA},
abstract = {From the text: A symmetric polynomial is a polynomial in one or more variables in which swapping any pair of variables leaves the polynomial unchanged. For example, $f(x,y,z)=xy+xz+yz$ is a symmetric polynomial. If we interchange the variables $x$ and $y$, we obtain $yx+yz+xz$, which is the same as $f(x,y,z)$; likewise, swapping $x$ and $z$ (or $y$ and $z$) returns the original polynomial. These polynomials arise in many areas of mathematics, including Galois theory and combinatorics, but they are rarely taught in a high school curriculum. In this article, we describe an application of symmetric polynomials to a familiar problem in coordinate geometry, thus introducing this powerful tool in a context that is accessible to high school students.},
msc2010 = {G74xx (H24xx)},
identifier = {2016c.00767},
}