Virtual Reality (VR)

Differential geometry provides a mathematical framework for modeling continuous spaces and their transformations, offering a rigorous language to describe the shape of data and the dynamics of systems operating within complex environments. This field extends classical calculus to curved spaces, enabling the analysis of properties that remain invariant under smooth deformations, which is essential for understanding systems that do not conform to Euclidean assumptions. Within t

Proprioception constitutes the internal awareness of body position and movement in biological systems, enabling coordinated motion without visual feedback, a mechanism that robotics seeks to replicate through engineering rather than evolution. Biological proprioception relies on muscle spindles, Golgi tendon organs, and joint receptors that feed continuous data to the central nervous system, creating a real-time map of the body's configuration in space. In robotics, proprioce