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In this work we provide an algorithm approximating the tangent bivector at apoint of a smooth surface through inscribed triangles converging to the point,regardless their form or position with respect to the tangent plane. Thisresult is obtained approximating Jacobian determinants of smooth planetransformations at a point x through nondegenerate triangles converging to x.We can also approximate the area of a portion of a smooth surface, through aslightly modified notion of area of inscribed triangular polyhedra approachingthe surface (without any kind of constraint due to the Schwarz paradox).

Algorithms, unaffected by the Schwarz paradox, approximating tangent planes and area of smooth surfaces via inscribed triangular polyhedra