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An ellipsograph is a trammel of Archimedes intended to draw, cut, or machine ellipses, e.g. in wood or other sheet materials. An ellipsograph has the appropriate instrument (pencil, knife, router, etc.) attached to the rod. Usually the distances a and b are adjustable, so that the size and shape of the ellipse can be varied.
In geometry, the elliptic coordinate system is a two-dimensional orthogonal coordinate system in which the coordinate lines are confocal ellipses and hyperbolae. The two foci F 1 {\displaystyle F_{1}} and F 2 {\displaystyle F_{2}} are generally taken to be fixed at − a {\displaystyle -a} and + a {\displaystyle +a} , respectively, on the x ...
An ellipse has two axes and two foci Unlike most other elementary shapes, such as the circle and square , there is no algebraic equation to determine the perimeter of an ellipse . Throughout history, a large number of equations for approximations and estimates have been made for the perimeter of an ellipse.
The outer edge of the dark blue line is an ellipse with the same eccentricity as that of Earth. For comparison, the light blue circle within has a diameter equal to the ellipse's minor axis. The red curve represents the Karman line 100 km (62 mi) above sea level, while the yellow band denotes the altitude range of the ISS in low Earth orbit
The equations in the Cartesian plane : + = = define, respectively, an ellipse and a hyperbola. In each case, the x and y axes are the principal axes. This is easily seen, given that there are no cross-terms involving products xy in either expression.
A spheroid. A great ellipse is an ellipse passing through two points on a spheroid and having the same center as that of the spheroid. Equivalently, it is an ellipse on the surface of a spheroid and centered on the origin, or the curve formed by intersecting the spheroid by a plane through its center. [1]