Some properties of the curves xn +yn=1 with even exponents

• Autorzy: Fidytek I.
• Języki publikacji: EN

Abstrakty

EN

We present parametric equations for the curve xn + yn = 1 with even exponents, in terms of the double area of the sector bounded by the arc between (1,0) and (x, y) and the radius vectors of these points. We determine also the area enclosed by this curve.

Słowa kluczowe

EN

curves; parametric equations

PL

krzywe; równania parametryczne

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2010
• Tom: Vol. 43, nr 1
• Strony: 89--96
• Opis fizyczny: Bibliogr. 4 poz.

Twórcy

autor

Fidytek I.

• Institute of Mathematics and Computer Science Jan Długosz University Armii Krajowej 13/15 42-200 Częstochowa, Poland,

Bibliografia

• [1] R. Tardiff, The surfaces z=(xn+yn)1/n are isothermal, Twenty-third International Symposium on Functional Equations (1985), Garganano-Italy.
• [2] A. Levin, A geometric interpretation of an infinite product for the Lemniscate constant, Amer. Math. Monthly 113 (2006), 510-520
• [3] I. Adamaszek, On generalized sine and cosine functions, Demonstratio Math. 38 (1995), 263-270.
• [4] I. N. Bronstein, K. A. Semendjajew, G. Musiol, H. Mühlig, Taschenbuch der Mathematik, Deutsch Harri GmbH, 2001