👉 Contact math is a branch of mathematics that deals with the study of curves and surfaces in higher-dimensional spaces, particularly focusing on their intersections and tangencies. It extends the principles of differential geometry to more complex geometric objects, providing tools to analyze how these surfaces and curves interact with each other. In contact geometry, the concept of a contact structure is central: it is a maximally non-integrable distribution on a manifold, essentially defining a region where no "sliding" or "twisting" can occur without violating the non-integrability condition. This leads to the study of contact manifolds, which are smooth manifolds equipped with a contact structure that satisfies this condition. Contact math has profound implications in various fields, including theoretical physics, particularly in the study of Hamiltonian systems and symplectic geometry, as well as in robotics and computer vision for motion planning and surface analysis.
