The fine-structure constant, α, unites fundamental aspects of electromagnetism, relativity, and quantum physics. As such, it is one of the most important constants in nature. However, why it has the value of approximately 1/137 has been a mystery since it was first identified more than 100 years ago. This study explores the possibility that the value of α is linked to the spacetime geometry of the electromagnetic field between two elementary charges, connecting the smooth manifold responsible for gravity with the discreteness of the electromagnetic field. In a step-by-step manner, the study presents a logical basis for the establishment of a particular equation for α, connecting concepts from general relativity and the Standard Model, and data from experiments to measure the value of elementary electric charge. It is shown how the equation and the model upon which it is built can help explain the Landau pole in such a way that avoids the substantial problem the pole creates in quantum electrodynamics.