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A. Kneser,Bemerkungen über die Anzahl der Extreme der Krümmung auf gechlossenen Kurven und über verwandte Fragen in einer nicht-euklidischen Geometrie [Festschrift zum 70. Geburtstag vonH. Weber, pp. 170–180].
T. Kubota,Über die Schwerpunkte der korwexen geschlossenen Kurven und Flächen [Tôhoku Mathematical Journal, vol. 14 (1918), pp. 20–27], p. 23. Also seeS. Nakajima,The circle and the straight line nearest to n given points, n given straight lines or a given curve [Tôhoku Mathematical Journal, vol. 19 (1921), pp. 11–20], p. 18, andT. Hayashi,on Steiner’s curvature-centroid [Science Reports of the Tôhoku Imperial University, vol. 12 (1924), pp. 109–132].
A. Hurwitz,Über die Fourier schenkonstanten integrierbarer Funktionen [Mathematische Annalen, Bd. 57 (1903), S. 425–446], p. 444.
I have given another proof for this theorem. SeeT. Hayashi,The extremal chords of an oval [Tôhoku Mathematical Journal, vol. 22 (1923), pp. 387–393], p. 393.
Blaschke: Archiv d. Math. und Physik, vol. 26 (1917) Aufgabe 540, p. 65; andSzegö: Archiv, vol. 28 (1920),Lösung, p. 183.W. Süss gave another proof which is to be published in a near future issue of Tôhoku Math. Jour.
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Hayashi, T. Some geometrical applications of fourier series. Rend. Circ. Matem. Palermo 50, 96–102 (1926). https://doi.org/10.1007/BF03014758
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DOI: https://doi.org/10.1007/BF03014758