Journal of the Mathematics Council of the Alberta Teachers’ Association
Volume 45 Issue 2, June 2008
28 – 35
William G Mandras
Algebra Through Symmetry is a visual method that was prevalent at the dawn of the mathematical sciences. At the University of Alexandria, in 310 BC, Euclid’s students used symmetry in the solution of equations. In the equation 2x = 8, each term was presumed to be an area and a geometric diagram was constructed. Considering Euclid’s fourth axiom, “Things which coincide with one another are equal to one another,” a student would conclude that equality requires that the two rectangular areas are equal; therefore, x must coincide with 4.
