# Geometric Constructions with Ellipses

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One of the most useful geometric curves is the parabola. Every parabola has two important parts: its focus point and its axis. Paraboloids are very useful objects and are found all around. They are used in two important ways for sending and for receiving. In sending, if a light source is placed...

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In the Euclidean space Eï¿½, it is well known that normal curves, i.e., curves with position vector always lying in their normal plane, are spherical curves [3]. Necessary and sufficient conditions for a curve to be a spherical curve in Euclidean 3-space are given in [10] and [11]. In this...

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Let \$C\$ be an irreducible, smooth, projective curve of genus \$g$\backslash$geqslant 3\$ over the complex field \$$\backslash$mathbb\{C\}\$. The curve \$C\$ is called \{$\backslash$em bielliptic\} if it admits a degree-two morphism \$$\backslash$pi$\backslash$colon C$\backslash$longrightarrow...

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We describe the dynamics of the Kirchhoff ellipse by formulating a nonlinear equation for the boundary of a perturbed vortex patch in elliptical coordinates. We demonstrate that in the regime for which the linearized equation of motion is unstable, the nonlinear dynamics of a rather general...

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The idea of the Wintner method relate to the problem of existence in the Newtonian many body problem of homographical solutions, similar to conic sections. We have generalised this idea on a case of other classes of homographical solutions, similar to curves, described by the Wejerstrass function.