radiation such that the tip of the electric field vector describes an ellipse in any fixed plane intersecting, and normal to, the direction of propagation...

concentric elliptic cone. It is the spherical analog of a conic section (ellipse, parabola, or hyperbola) in the plane, and as in the planar case, a spherical...

Further, the orthogonal trajectories of these ellipses comprise the elliptic curves with j ≤ 1, and any ellipse in H 2 {\displaystyle \mathbb {H} ^{2}} described...

"Courbes 2D" at Encyclopédie des Formes Mathématiques Remarquables "Courbes 3D" at Encyclopédie des Formes Mathématiques Remarquables An elementary treatise...

from a semi-ellipse. To meet the curvature condition, the semi-ellipse should be bounded by the semi-major axis of its ellipse, and the ellipse should have...

but the segment from any point in the plane to the nearest point on an ellipse of positive eccentricity cannot in general be constructed. See Note that...

14 shows how to draw an ellipse through five given points, and Prop. 15 gives a simple construction for the axes of an ellipse when a pair of conjugate...

prior to the invention of analytic geometry. His definitions of the terms ellipse, parabola, and hyperbola are the ones in use today. With his predecessors...

In celestial mechanics, this is usually a Keplerian ellipse. Under Newtonian gravity, an ellipse is exactly correct when there are only two gravitating...

geodesics on the ellipses X = 0 and Z = 0 are stable (a geodesic initially close to and nearly parallel to the ellipse remains close to the ellipse), the closed...

corresponding limaçon will have an inner loop, and if the conic is an ellipse then the corresponding limaçon will have no loop. The conchoid of a circle...

into another. In this way, an ellipse becomes a parabola when a focus moves toward infinity, and when two foci of an ellipse merge into one another, a circle...

formulae in trigonometry and geometry, especially those concerning circles, ellipses and spheres. It is also found in formulae from other topics in science...

Encyclopédie des Formes Mathématiques Remarquables "Quartique Bicirculaire Rationnelle" at Encyclopédie des Formes Mathématiques Remarquables Stubbs, J...

Correspondance 1691–1695 (1905). Tome XI: Travaux mathématiques 1645–1651 (1908). Tome XII: Travaux mathématiques pures 1652–1656 (1910). Tome XIII, Fasc. I:...

{\pi }{4}}} Now considering the circumference C {\displaystyle C} of the ellipse with axes 2 {\displaystyle {\sqrt {2}}} and 1 {\displaystyle 1} , satisfying...

that allows users to draw any conic section: straight lines, circles, ellipses, parabolas and hyperbolas. It is likely that al-Qūhī invented the device...

Thus, we obtain 4 ellipses: the 4 planar intersections with the auxilliary ellipsoid. These ellipses all exist on the wavevector surface...

phase-space trajectory that traces out an ellipse corresponding to the particle's energy. The frequency at which the ellipse is traced is given by the ω {\displaystyle...

four vertices. An ellipse has exactly four vertices: two local maxima of curvature where it is crossed by the major axis of the ellipse, and two local minima...

question of the Problem of Three Bodies)": see d'Alembert, "Opuscules Mathématiques", vol. 2, Paris 1761, Quatorzième Mémoire ("Réflexions sur le Problème...

theory of curvilinear coordinates and his notation and study of classes of ellipse-like curves, now known as Lamé curves or superellipses, and defined by...

c} remains constant. Every triangle has a unique Steiner inellipse – an ellipse inside the triangle and tangent to the midpoints of the three sides of...

surface of revolution of an elliptic catenary: that is, by rolling an ellipse along a fixed line, tracing the focus, and revolving the resulting curve...

at Aix-Marseille University since 1995, and directs the Institut de Mathématiques de Marseille. She earned her doctorate in 1986 at Claude Bernard University...

"Hippopede" at 2dcurves.com "Courbes de Booth" at Encyclopédie des Formes Mathématiques Remarquables "The Hippopede of Proclus" at The National Curve Bank...

standardized scores Estimated from the balloon rule Related to the bivariate ellipses of isoconcentration Function of test statistics from designed experiments...

in the sky are particular cases of the same mathematical object of an ellipse, and postulated the universal law of gravitation on the basis of a single...

Steiner circumellipse of triangle ABC, also called the Steiner ellipse, is the ellipse of least area that passes through the vertices A, B and C. The...

of explicitly constructing a conformal mapping from the interior of an ellipse to the unit disk. His solution, which combined an early work on elliptic...