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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). ...

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

To inscribe an equilateral triangle in an ellipse, place the top polygon vertex at (0,b), then solve to find the (x,y) coordinate of the other two vertices. ...

A quadratic equation is a second-order polynomial equation in a single variable x ax^2+bx+c=0, (1) with a!=0. Because it is a second-order polynomial equation, the ...

A connection on a vector bundle pi:E->M is a way to "differentiate" bundle sections, in a way that is analogous to the exterior derivative df of a function f. In particular, ...

The involute of an ellipse specified parametrically by x = acost (1) y = bsint (2) is given by the parametric equations x_i = ...

The parallel curves for (outward) offset k of an ellipse with semi-axis lengths a and b are given by x_p = (a+(bk)/(sqrt(a^2sin^2t+b^2cos^2t)))cost (1) y_p = ...

The involute of a parabola x = at^2 (1) y = at (2) is given by x_i = -(atsinh^(-1)(2t))/(2sqrt(4t^2+1)) (3) y_i = a(1/2t-(sinh^(-1)(2t))/(4sqrt(4t^2+1))). (4) Defining ...

For a parabola oriented vertically and opening upwards, the vertex is the point where the curve reaches a minimum.

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 ...