Perpendicular diameters of a circle or hyperbolic-orthogonal diameters of a hyperbola
In geometry, two diameters of a conic section are said to be conjugate if each chord parallel to one diameter is bisected by the other diameter. For example, two diameters of a circle are conjugate if and only if they are perpendicular.
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geometry, two diameters of a conic section are said to be conjugate if each chord parallel to one diameter is bisected by the other diameter. For example...
measuring diameters Conjugate diameters – Perpendicular diameters of a circle or hyperbolic-orthogonal diameters of a hyperbola Diameter (group theory) – measure...
{\displaystyle {\overline {P_{2}Q_{2}}}} . Conjugatediameters in an ellipse generalize orthogonal diameters in a circle. In the parametric equation for...
pair of conjugatediameters are taken as new axes, and a new unit of length is taken proportional to the length of either of these diameters." On this...
plane in an asymptote exchanges the conjugates. The conjugate hyperbola arises in the study of conjugatediameters of conic sections. Elements of Dynamic...
{1}{2}}{\sqrt {\frac {ab}{ab-1}}}\;(u_{1}-v_{1},u_{2}-v_{2})\;} are two conjugate half diameters and the inellipse has the more common trigonometric parametric...
two diameters are said to be conjugate if and only if the tangent line to the ellipse at an endpoint of one diameter is parallel to the other diameter. Each...
follows: The diameters or conjugates of the pelvis are measured at the pelvic inlet and outlet and as oblique diameters. Two diameters may be measured...
transformation". This diagram included the unit hyperbola, its conjugate, and a pair of conjugatediameters. Since the 1960s a version of this more complete configuration...
particular, this action swaps the unit hyperbola with its conjugate and swaps pairs of conjugatediameters of the hyperbolas. In terms of the hyperbolic angle...
diameter. A conjugatediameter bisects the chords, being placed between the centroid and the tangent point. Moreover, both diameters are conjugate to each...
the theory after the underlying principle. Background independence Conjugatediameters Cosmic microwave background radiation Equivalence principle Galilean...
Osgood and Graustein used the rectangular hyperbola, its conjugate hyperbola, and conjugatediameters to rationalize tie rods at 15 degree radial spacing,...
mathematical notions preceded physical interpretation. For instance, conjugatediameters of a conjugate hyperbolas are related as space and time. The principle of...
terminology stems from the use of two conjugate hyperbolas in the pseudo-Euclidean plane: conjugatediameters of these hyperbolas are hyperbolic-orthogonal...
Hence semi diameter S D {\displaystyle SD} is conjugate to S C {\displaystyle SC} . With help of this pair of conjugate semi diameters the ellipse can...
consists of drawing the images of two perpendicular diameters of the circle, which are conjugatediameters of the image ellipse, determining the axes of the...
touching a given ellipse (to be understood: at the endpoints of conjugatediameters) are equal in area. Then follows Newton's main subject-matter, labelled...
a simple construction for the axes of an ellipse when a pair of conjugatediameters are given. Pappus's Collection was virtually unknown to the Arabs...
electrical engineering:—Details the development of electrical engineering Conjugatediameters § Of hyperbola:–Succinct expression of the principle of relativity...
lines at A and D) uniquely determine the conic. If another diameter (and its conjugatediameter) are used instead of the major and minor axes of the ellipse...
volcano's crater is elliptical with a transverse diameter measuring 478 m (1,568 ft) and a conjugatediameter measuring 410 m (1,350 ft). The crater has an...
In projective geometry, the harmonic conjugate point of a point on the real projective line with respect to two other points is defined by the following...
helix angle is greater for larger gear diameters. It is understood to be measured at the standard pitch diameter unless otherwise specified. Hobbing is...
procedure retrieves the semi-axes of an Ellipse from any pair of conjugatediameters. This method is known since 1845, when it was published within a...
perpendicular to the conjugate axis and to each directrix. The product of the perpendicular distances from a point P on a hyperbola or on its conjugate hyperbola...
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