\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2016c.00767}
\itemau{Matsuura, Ryota; Sword, Sarah}
\itemti{Illuminating coordinate geometry with algebraic symmetry.}
\itemso{Math. Teach. (Reston) 108, No. 6, 470-473 (2015).}
\itemab
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.
\itemrv{~}
\itemcc{G74 H24}
\itemut{symmetric polynomials; coordinate geometry; analytic geometry; upper secondary; triangles; proofs; centroid; center of mass; medians; equations of straight lines; parametric equations; generalization; tetrahedra; concurrency; reasoning}
\itemli{http://www.nctm.org/Publications/mathematics-teacher/2015/Vol108/Issue6/Illuminating-Coordinate-Geometry-with-Algebraic-Symmetry/}
\end