Ellipse Metric properties
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well. All metric properties given below refer to an ellipse with equation except for the section on the area enclosed by a tilted ellipse, where the...
Diameter (redirect from Metric diameter)the ellipse. For example, conjugate diameters have the property that a tangent line to the ellipse at the endpoint of one diameter is parallel to the conjugate...
This means that the MacAdam ellipses become nearly (but not exactly) circular in these spaces. Using a Fisher information metric, da Fonseca et al. investigated...
Mass (redirect from Metric unit of weight)orbits as following elliptical paths with the Sun at a focal point of the ellipse. Kepler discovered that the square of the orbital period of each planet...
Sphere (section Metric spaces)Cohn-Vossen describe eleven properties of the sphere and discuss whether these properties uniquely determine the sphere. Several properties hold for the plane...
Area (redirect from Area of an ellipse)r^{2}.} The formula for the area enclosed by an ellipse is related to the formula of a circle; for an ellipse with semi-major and semi-minor axes x and y...- Generalized conic (redirect from Generalized ellipse)defined by a property which is a generalization of some defining property of the classical conic. For example, in elementary geometry, an ellipse can be defined...
- Directional component analysis (section Properties)following properties: Of all the points on the diagonal line, it is the one with the highest probability density Of all the points on the ellipse, it is...
Astroid (section Metric properties)cubocycloid, and paracycle. It is nearly identical in form to the evolute of an ellipse. If the radius of the fixed circle is a then the equation is given by x...- This metric allows quantified examination of a notion that formerly could only be described with adjectives. Quantification of these properties is of...
Map projection (section Metric properties of maps)projections exist in order to preserve some properties of the sphere-like body at the expense of other properties. The study of map projections is primarily...
Space (mathematics) (section Metric and uniform spaces)into similar figures. For example, all circles are mutually similar, but ellipses are not similar to circles. A third equivalence relation, introduced by...
all equilateral triangles are similar to each other. On the other hand, ellipses are not all similar to each other, rectangles are not all similar to each...- Randomized Hough transform (section Ellipse fitting)similarities between the newly detected ellipse and the ones already stored in accumulator array. Different metrics can be used to calculate the similarity...
Inscribed figure (section Properties)same thing as "figure G is circumscribed about figure F". A circle or ellipse inscribed in a convex polygon (or a sphere or ellipsoid inscribed in a...
Shape (section Properties)Other common shapes are points, lines, planes, and conic sections such as ellipses, circles, and parabolas. Among the most common 3-dimensional shapes are...- Quasiconformal mapping (section Properties)between plane domains which to first order takes small circles to small ellipses of bounded eccentricity. Intuitively, let f : D → D′ be an orientation-preserving...
- pseudo-Riemannian metric on a manifold. It can be considered, broadly, as a measure of the degree to which the geometry of a given metric tensor differs...
- Elliptic geometry (category Metric geometry)connection with the curve called an ellipse, but only a rather far-fetched analogy. A central conic is called an ellipse or a hyperbola according as it has...
Mollweide projection (section Properties)the whole earth is depicted in a proportional 2:1 ellipse. The proportion of the area of the ellipse between any given parallel and the equator is the...
- This important property gives a first example how metric properties are connected with projective ones. [§ 21. Harmonic properties of the complete quadrilateral
- condition requires that infinitesimal circles be taken into infinitesimal ellipses of uniformly bounded eccentricity. (1956). "An outline of the theory of
- are the two coordinate axes. Hyperbolas share many of the ellipses' analytical properties such as eccentricity, focus, and directrix. Typically the correspondence