plane curves

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1: 19.30 Lengths of Plane Curves

§19.30 Lengths of Plane Curves

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§19.30(i) Ellipse

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§19.30(ii) Hyperbola

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§19.30(iii) Bernoulli’s Lemniscate

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2: 21.10 Methods of Computation

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Tretkoff and Tretkoff (1984). Here a Hurwitz system is chosen to represent the Riemann surface.

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Deconinck and van Hoeij (2001). Here a plane algebraic curve representation of the Riemann surface is used.

3: 22.18 Mathematical Applications

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§22.18(i) Lengths and Parametrization of Plane Curves

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4: 21.7 Riemann Surfaces

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§21.7(i) Connection of Riemann Theta Functions to Riemann Surfaces

… ►Belokolos et al. (1994, §2.1)), they are obtainable from plane algebraic curves (Springer (1957), or Riemann (1851)). …Equation (21.7.1) determines a plane algebraic curve in ${ℂ}^2$, which is made compact by adding its points at infinity. …

5: Bibliography G

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Riemann surfaces, plane algebraic curves and their period matrices. J. Symbolic Comput. 26 (6), pp. 789–803.

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External Links:

ISSN 0747-7171, Document, MathReview (Gabino González Díez), ZentralBlatt

Referenced by:

1st item.

Encodings:

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6: 10.41 Asymptotic Expansions for Large Order

… ►The curve $E_{1}B{E}_2$ in the $z$-plane is the upper boundary of the domain $𝐊$ depicted in Figure 10.20.3 and rotated through an angle $-\frac{1}{2}\pi$. …

7: Bibliography B

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Plane Algebraic Curves. Birkhäuser Verlag, Basel.

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Notes:

Translated from the German by John Stillwell

External Links:

ISBN 3-7643-1769-8, MathReview, ZentralBlatt

Referenced by:

§21.7(i).

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8: Philip J. Davis

… ►Moreover, a cutting plane feature allows users to track curves of intersection produced as a moving plane cuts through the function surface. …

9: 23.20 Mathematical Applications

… ►If $a,b\in ℝ$, then $C$ intersects the plane ${ℝ}^2$ in a curve that is connected if $\mathrm{\Delta }\equiv 4a^3+27b^2>0$; if , then the intersection has two components, one of which is a closed loop. …

10: 1.6 Vectors and Vector-Valued Functions

… ►and $S$ be the closed and bounded point set in the $(x,y)$ plane having a simple closed curve $C$ as boundary. …