The fine structure constant is shown to arise naturally in the course of altering the symmetry of two algebraic identities. Specifically, the symmetry of the identity M² = M² is "broken" by making the substitution M → M − y on its left side, and the substitution Mⁿ → Mⁿ − x^p on its right side, where p equals the order of the identity; these substitutions convert the above identity into the equation (M − y)² = M² − x². These same substitutions are also applied to the only slightly more complicated identity (M / N)³ + M² = (M / N)³ + M² to produce this second equation (M − y)³ / N³ + (M − y)² = (M³ − x³) / N³ + M² − x³. These two equations are then shown to share a mathematical property relating to dy/dx, where, on the second equation�s right side this property helps define the special case (M³ − x³) / N³ + M² − x³ = (10³ − 0.1³) / 3³ + 10² − 0.1³ = 137.036, which incorporates a value close to the experimental fine structure constant inverse.