Search Results for "ellipse"

The circumcircle of an ellipse, i.e., the circle whose center concurs with that of the ellipse and whose radius is equal to the ellipse's semimajor axis.

The greatest radial distance of an ellipse as measured from a focus. Taking v=pi in the equation of an ellipse r=(a(1-e^2))/(1+ecosv) gives the apoapsis distance r_+=a(1+e). ...

The smallest radial distance of an ellipse as measured from a focus. Taking v=0 in the equation of an ellipse r=(a(1-e^2))/(1+ecosv) gives the periapsis distance r_-=a(1-e). ...

Lockwood (1957) terms the ellipse negative pedal curve with pedal point at the focus "Burleigh's oval" in honor of his student M. J. Burleigh, who first drew his attention to ...

The angle obtained by drawing the auxiliary circle of an ellipse with center O and focus F, and drawing a line perpendicular to the semimajor axis and intersecting it at A. ...

An ellipsoidal section is the curve formed by the intersection of a plane with an ellipsoid. An ellipsoidal section is always an ellipse.

If P(x,y) and P(x^',y^') are two points on an ellipse (x^2)/(a^2)+(y^2)/(b^2)=1, (1) with eccentric angles phi and phi^' such that tanphitanphi^'=b/a (2) and A=P(a,0) and ...

_2F_1(-1/2,-1/2;1;h^2) = sum_(n=0)^(infty)(1/2; n)^2h^(2n) (1) = 1+1/4h^2+1/(64)h^4+1/(256)h^6+... (2) (OEIS A056981 and A056982), where _2F_1(a,b;c;x) is a hypergeometric ...

There are two curves commonly known as the Lamé curve: the ellipse evolute and the superellipse.

The semimajor axis (also called the major semi-axis, major semiaxis, or major radius) of an ellipse (or related figure) is half its extent along the longer of the two ...