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On Convexity and Approximating the Perimeter of an Ellipse

DOI: 10.4236/oalib.1100332, PP. 1-7

Subject Areas: Algebraic Geometry, Geometry, Function Theory

Keywords: Convexity, Minimum Length, Approximation, Inequalities, Perimeter of the Ellipse

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In the first part of this work, a convex partition of a compact subset is constructed. Minimum-length surrounding curve and minimum-area surrounding surfaces for a compact set are constructed too. In the second part, one writes the perimeter of an ellipse as the sum of an alternate series. On the other hand, we deduce related “sandwich” inequalities for the perimeter, involving Jensen’s inequality and logarithmic function respectively. We discuss the values of the ordinate of the gravity center of the upper semiellipse at the ends of the positive semiaxes, in terms of the scale ratio .

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Olteanu, O. (2014). On Convexity and Approximating the Perimeter of an Ellipse. Open Access Library Journal, 1, e332. doi:


[1]  Almkvist, G. and Berndt, B. (1988) Gauss, Landen, Ramanujan, the Arithmetic Geometric Mean, Ellipses, π, and the Ladies Diary. The American Mathematical Monthly, 95, 585-608.
[2]  Chandrupatla, T.R. and Osler, T.J. (2010) The Perimeter of an Ellipse. The Mathematical Scientist, 35, 122-131.
[3]  Barnard, R.W., Pearce, K. and Schovanec, L. (2001) Inequalities for the Perimeter of an Ellipse. Journal of Mathemat- ical Analysis and Applications, 260, 295-306.
[4]  Neumann, M. (1977) On the Strassen Disintegration Theorem. Archiv der Mathematik, 29, 413-420.
[5]  Udri?te, C., ?evy, I. and Arsinte, V. (2010) Minimal Surfaces between Two Points. Journal of Advanced Mathematical Studies, 3, 105-116.
[6]  Phelps, R.R. (1966) Lectures on Choquet’s Theorem. D. Van Nostrand Company, Inc., Princeton.
[7]  Boboc, N. and Bucur, Gh. (1976) Convex Cones of Continuous Functions on Compact Spaces. Academiei, Bucharest (in Romanian).
[8]  Deville, R., Fonf, D. and Hájek, P. (1998) Analytic and Polyhedral Approximation of Convex Bodies in Separable Polyhedral Banach Spaces. Israel Journal of Mathematics, 105, 139-154.
[9]  Niculescu, C. and Popa, N. (1981) Elements of Theory of Banach Spaces. Academiei, Bucharest (in Romanian).
[10]  Olteanu, O. (1994) Uniform Approximation of Certain Continuous Functions. Studii si Cercetari Matematice (Mathematical Reports), 46, 533-541.
[11]  Rudin, W. (1987) Real and Complex Analysis. 3rd Edition, McGraw-Hill, Inc., New York.


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