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This circle corresponds to the smaller circle in a Tusi couple. The point midway between the pivots orbits in a circle around the point where the channels cross. This circle is also a special case of an ellipse. Here the axes are of equal length. The diameter of the circle is equal to the distance between the pivots.
The classic applications of elliptic coordinates are in solving partial differential equations, e.g., Laplace's equation or the Helmholtz equation, for which elliptic coordinates are a natural description of a system thus allowing a separation of variables in the partial differential equations. Some traditional examples are solving systems such ...
A circle of radius a compressed to an ellipse. A sphere of radius a compressed to an oblate ellipsoid of revolution. Flattening is a measure of the compression of a circle or sphere along a diameter to form an ellipse or an ellipsoid of revolution respectively. Other terms used are ellipticity, or oblateness.
A circle viewed from a side angle looks like an ellipse: that is, the ellipse is the image of a circle under parallel or perspective projection. The ellipse is also the simplest Lissajous figure formed when the horizontal and vertical motions are sinusoids with the same frequency: a similar effect leads to elliptical polarization of light in ...
For example, on a triaxial ellipsoid, the meridional eccentricity is that of the ellipse formed by a section containing both the longest and the shortest axes (one of which will be the polar axis), and the equatorial eccentricity is the eccentricity of the ellipse formed by a section through the centre, perpendicular to the polar axis (i.e. in ...
The aspect ratio of the resulting ellipse is a function of the phase shift between the input and output, with an aspect ratio of 1 (perfect circle) corresponding to a phase shift of ±90° and an aspect ratio of ∞ (a line) corresponding to a phase shift of 0° or 180°. [citation needed]
The solid curve is the ellipse, with m = 1 − 1/b 2 and u = F(φ,m) where F(⋅,⋅) is the elliptic integral of the first kind (with parameter =). The dotted curve is the unit circle. Tangent lines from the circle and ellipse at x = cd crossing the x-axis at dc are shown in light grey.
The distance formula is homogeneous in each variable, with d(λu, μv) = d(u, v) if λ and μ are non-zero scalars, so it does define a distance on the points of projective space. A notable property of the projective elliptic geometry is that for even dimensions, such as the plane, the geometry is non-orientable. It erases the distinction ...