Geodesic
A sharpening of a discrete analog of Wirtinger's and isoperimetric inequalities
Mathematica Bohemica, Tome 117 (1992) no. 4, pp. 425-428

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MR Zbl
A sharpening of a discrete case of Wirtinger's inequality is given. It is then used to sharpen the isoperimetric unequality for polygons.
A sharpening of a discrete case of Wirtinger's inequality is given. It is then used to sharpen the isoperimetric unequality for polygons.
DOI : 10.21136/MB.1992.126056
Classification : 51M16, 52A40
Keywords: closed $n$-gons; inequalities; Wirtinger's inequality; trigonometric polynomials 
Pech, Pavel. A sharpening of a discrete analog of Wirtinger's and isoperimetric inequalities. Mathematica Bohemica, Tome 117 (1992) no. 4, pp. 425-428. doi: 10.21136/MB.1992.126056
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[1] L. Boček: Isoperimetrische Ungleichungen für räumliche Kurven und Polygone. Čas. pro pěst. mat. 104 (1979), 86-92. | MR

[2] K. Fan O. Taussky J. Todd: Discrete analogs of inequalities of Wirtinger. Monatsh. Math. 50 (1955), 73-90. | MR

[3] Z. Nádeník: Die Verchärfung einer Ungleichung von Frobenius für den gemischten Flächeninhalt der konvexen ebenen Bereiche. Čas. pro pěst, mat. 90 (1965), 220-225. | MR

[4] J. Novotná: A sharpening of discrete analogues of Wirtinger's inequality. Čas. pro pěst. mat. 108 (1983), 70-77. | MR | Zbl

[5] I. J. Schoenberg: The finite Fourier series and elementary geometry. Amer. Math. Monthly 57 (1950), 390-404. | DOI | MR | Zbl

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