This paper presents an approach to the theory of Riemannian manifolds without using coordinates. Curved spaces are approximated by higher-dimensional analogs of polyhedra. This method allows for a simplified model of complex topologies, such as Wheeler's wormhole, and provides deeper geometrical insight. In two dimensions, surfaces are approximated by polyhedra. A general surface can be considered as the limit of a sequence of polyhedra with increasing numbers of faces. Although a rigorous definition of limit is not provided, it is expected that any surface can be arbitrarily approximated by a suitable polyhedron. The integral Gaussian curvature of a triangle is defined by the difference between the sum of its internal angles and π. For a sphere, this curvature is related to the area of the triangle and the radius of the sphere. As the triangle shrinks to a point, the local Gaussian curvature is defined as the limit of the curvature divided by the area. The curvature of a polyhedron is defined using the concept of deficiency at each vertex. If a triangle lies entirely on a face or does not contain any vertex, the curvature is zero. If a triangle contains a vertex, the curvature is determined by the deficiency of that vertex. The total curvature of a polyhedron is the sum of the curvatures at all its vertices. The Gauss-Bonnet theorem is expressed as the sum of the curvatures at all vertices equals 2π(2 - N), where N is the genus of the polyhedron. This theorem is closely related to Euler's formula for the genus. The connection between the curvature and the topology of the polyhedron is clear, and the results can be summarized using the concept of curvature as a Dirac-type distribution.This paper presents an approach to the theory of Riemannian manifolds without using coordinates. Curved spaces are approximated by higher-dimensional analogs of polyhedra. This method allows for a simplified model of complex topologies, such as Wheeler's wormhole, and provides deeper geometrical insight. In two dimensions, surfaces are approximated by polyhedra. A general surface can be considered as the limit of a sequence of polyhedra with increasing numbers of faces. Although a rigorous definition of limit is not provided, it is expected that any surface can be arbitrarily approximated by a suitable polyhedron. The integral Gaussian curvature of a triangle is defined by the difference between the sum of its internal angles and π. For a sphere, this curvature is related to the area of the triangle and the radius of the sphere. As the triangle shrinks to a point, the local Gaussian curvature is defined as the limit of the curvature divided by the area. The curvature of a polyhedron is defined using the concept of deficiency at each vertex. If a triangle lies entirely on a face or does not contain any vertex, the curvature is zero. If a triangle contains a vertex, the curvature is determined by the deficiency of that vertex. The total curvature of a polyhedron is the sum of the curvatures at all its vertices. The Gauss-Bonnet theorem is expressed as the sum of the curvatures at all vertices equals 2π(2 - N), where N is the genus of the polyhedron. This theorem is closely related to Euler's formula for the genus. The connection between the curvature and the topology of the polyhedron is clear, and the results can be summarized using the concept of curvature as a Dirac-type distribution.