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Hyperbolic sector (area)

A hyperbolic sector is a region of the Cartesian plane {(x,y)} bounded by rays from the origin to two points (a, 1/a) and (b, 1/b) and by the hyperbola xy ... more

Solid angle (in spherical coordinates)

In geometry, a solid angle is the two-dimensional angle in three-dimensional space that an object subtends at a point. It is a measure of how large the ... more

Angle required to hit polar coordinate (x,y) - (projectile following a ballistic trajectory)

In physics, the ballistic trajectory of a projectile is the path that a thrown or launched projectile or missile without propulsion will take under the ... more

Pell's equation

Pell’s equation is a Diophantine equation (a polynomial equation in two or more unknowns ).
In Cartesian coordinates, the equation has the form ... more

Distance of the focal point from the center of an ellipse

Ellipse is a curve on a plane surrounding two focal points such that a straight line drawn from one of the focal points to any point on the curve and then ... more

Barycenter (Two-body problem)

barycentre; from the Greek βαρύ-ς heavy + κέντρ-ον centre) is the center of mass of two or more bodies that are orbiting each other, or the point around ... more

Prolate spheroid equation (c>a)

A spheroid, or ellipsoid of revolution is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid ... more

Oblate spheroid equation(c<a)

A spheroid, or ellipsoid of revolution is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid ... more

Epicycloid (The ordinate of a point)

In geometry, an epicycloid is a plane curve produced by tracing the path of a chosen point of a circle — called an epicycle — which rolls without slipping ... more

Center of mass (for a system of n-particles)

The center of mass of a distribution of mass in space is the unique point where the weighted relative position of the distributed mass sums to zero.
... more

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