Having shown in our previous works that the real-valued Schrodinger wave equation can be used to find mathematical functions to construct spacetime structures of quantum particles, in this work, we will discuss the possibility to formulate a real-valued Dirac equation in which all physical objects and all differential operators that are used to describe the dynamics of a particle are real quantities and, furthermore, since solutions to the Dirac equation are wavefunctions that have four components, it is possible to suggest that solutions to the real-valued Dirac equation should be interpreted as a parameterisation of 3-dimensional differentiable manifolds which are embedded submanifolds of the Euclidean space R^4.