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2016c.00767 Matsuura, Ryota Sword, Sarah Illuminating coordinate geometry with algebraic symmetry. Math. Teach. (Reston) 108, No. 6, 470-473 (2015). 2015 National Council of Teachers of Mathematics (NCTM), Reston, VA EN G74 H24 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
• http://www.nctm.org/Publications/mathematics-teacher/2015/Vol108/Issue6/Illuminating-Coordinate-Geometry-with-Algebraic-Symmetry/
• 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.