Approximation of Curves and Surfaces
Geometry of Euclidean Sets: Analytical, Stochastic and Hypertopological Aspects

AF223 V1 Article

Approximation of Curves and Surfaces
Geometry of Euclidean Sets: Analytical, Stochastic and Hypertopological Aspects

Author : Jean-Charles PINOLI

Publication date: June 10, 2026 | Lire en français

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15. Approximation of Curves and Surfaces

In mathematics, approximation theory deals with how functions (or sets) can be approximated “as well as possible” using simpler functions (or sets) and with the quantitative characterization of the errors introduced in the process.

15.1 Length of Jordan

Definition (Jordan length of a curve). Let C be a simple, bounded, rectifiable curve in $ℝ_{2}^{2}$ . The Jordan length of curve C, denoted by L _J (C), is defined as:

L_{J} (C) := \underset{P \in}{sup L (P)}

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Approximation of Curves and Surfaces

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page Euclidean set spaces

Boundaries of Euclidean sets

Bibliography

(1) - AUBIN (J.P.), FRANKOWSKA (H.) - Set-Valued Analysis, - Birkhäuser (1990).
(2) - BERGER (M.) - Geometry, - Springer, vol. 1 and 2, [1st ed., 1987] (2009).
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