# plane curves

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## 1—10 of 23 matching pages

##### 1: 19.30 Lengths of Plane Curves

###### §19.30 Lengths of Plane Curves

►###### §19.30(i) Ellipse

… ►###### §19.30(ii) Hyperbola

… ►###### §19.30(iii) Bernoulli’s Lemniscate

… ►##### 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.

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

…##### 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 ${\u2102}^{2}$, 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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##### 6: 10.41 Asymptotic Expansions for Large Order

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►The curve
${E}_{1}B{E}_{2}$ in the $z$-plane is the upper boundary of the domain $\mathbf{K}$ depicted in Figure 10.20.3 and rotated through an angle $-\frac{1}{2}\pi $.
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##### 7: Bibliography B

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Plane Algebraic Curves.
Birkhäuser Verlag, Basel.
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##### 8: Philip J. Davis

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►Moreover, a cutting plane feature allows users to track curves of intersection produced as a moving plane cuts through the function surface.
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##### 9: 23.20 Mathematical Applications

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►If $a,b\in \mathbb{R}$, then $C$ intersects the plane
${\mathbb{R}}^{2}$ in a curve that is connected if $\mathrm{\Delta}\equiv 4{a}^{3}+27{b}^{2}>0$; if $$, then the intersection has two components, one of which is a closed loop.
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##### 10: 1.6 Vectors and Vector-Valued Functions

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