The degree of freedom in mathematics, particularly in differential equations, refers to the number of independent values that can be chosen in a problem. This concept varies based on the specific scenario being analyzed. For instance, a bead on a circular frame has one degree of freedom due to the dependency between its x and y coordinates. In contrast, a point on a plane has two degrees of freedom, while a point in three-dimensional space has three. Additionally, a projectile's trajectory in three-dimensional space is considered one-dimensional since its position is determined by a single variable, time.