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}}}} . Conjugate diameters in an ellipse generalize orthogonal diameters in a circle. In the parametric equation for...

pair of conjugate diameters are taken as new axes, and a new unit of length is taken proportional to the length of either of these diameters." On this...

(1801–1868). Conjugate diameters appear always if a circle or an ellipse is projected parallelly (the rays are parallel) as images of orthogonal diameters of a...

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...

{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...

that the straight lines are conjugate diameters of both hyperbolas." "The two hyperbolas so constructed are called conjugate hyperbolas, and [the] last...

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...

diameter. A conjugate diameter bisects the chords, being placed between the centroid and the tangent point. Moreover, both diameters are conjugate to each...

Osgood and Graustein used the rectangular hyperbola, its conjugate hyperbola, and conjugate diameters to rationalize tie rods at 15 degree radial spacing,...

transformation". This diagram included the unit hyperbola, its conjugate, and a pair of conjugate diameters. Since the 1960s a version of this more complete configuration...

particular, this action swaps the unit hyperbola with its conjugate and swaps pairs of conjugate diameters of the hyperbolas. In terms of the hyperbolic angle...

the theory after the underlying principle. Background independence Conjugate diameters Cosmic microwave background radiation Equivalence principle Galilean...

mathematical notions preceded physical interpretation. For instance, conjugate diameters of a conjugate hyperbolas are related as space and time. The principle of...

This terminology stems from the use of conjugate hyperbolas in the pseudo-Euclidean plane: conjugate diameters of these hyperbolas are hyperbolic-orthogonal...

retrieved 2023-09-25 Karmakar, Sibdas; Karmakar (2022-02-16), "Diameters and Conjugate Diameters", Analytical Geometry: Two Dimensions, London: CRC Press,...

In numerical linear algebra, the conjugate gradient method is an iterative method for numerically solving the linear system A x = b {\displaystyle {\boldsymbol...

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...

principle of relativity speed of light faster-than-light biquaternion conjugate diameters four-vector four-acceleration four-force four-gradient four-momentum...

consists of drawing the images of two perpendicular diameters of the circle, which are conjugate diameters of the image ellipse, determining the axes of the...

a simple construction for the axes of an ellipse when a pair of conjugate diameters are given. Pappus's Collection was virtually unknown to the Arabs...

electrical engineering:—Details the development of electrical engineering Conjugate diameters § Of hyperbola:–Succinct expression of the principle of relativity...

lines at A and D) uniquely determine the conic. If another diameter (and its conjugate diameter) 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 conjugate diameter 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...

the other two codots of ABCD (page 25). Continuing with conics, conjugate diameters are straights, each of which is the polar of the figurative point...

procedure retrieves the semi-axes of an Ellipse from any pair of conjugate diameters. This method is known since 1845, when it was published within a...

axis of a hyperbola coincides with the major axis. In a hyperbola, a conjugate axis or minor axis of length 2 b {\displaystyle 2b} , corresponding to...