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In mathematics, a 3-sphere is a higher-dimensional analogue of a sphere. It consists of the set of points equidistant from a fixed central point in ... more

Descartes' theorem ( externally tangent circle to three given kissing circles)

In geometry, Descartes’ theorem states that for every four kissing, or mutually tangent, circles, the radii of the circles satisfy a certain ... more

Descartes' theorem ( internally tangent circle to three given kissing circles)

n geometry, Descartes’ theorem states that for every four kissing, or mutually tangent, circles, the radii of the circles satisfy a certain quadratic ... more

Tortuosity - alternative method

Tortuosity is a property of curve being tortuous (twisted; having many turns). There have been several attempts to quantify this property. ... more

Cauchy–Lorentz distribution (cumulative distribution function)

In probability and statistics,the Cauchy distribution, is a continuous probability distribution. The Cauchy distribution is often used in statistics as the ... more

Vertical Curve - Parabolic formula

Vertical Curves are the second of the two important transition elements in geometric design for highways, the first being Horizontal Curves. A vertical ... more

Angle of deflection of an end loaded cantilever beam

In engineering, deflection is the degree to which a structural element is displaced under a load. It may refer to an angle or a distance.
The angle of ... more

Kepler's equation - X coordinate

In orbital mechanics, Kepler’s equation relates various geometric properties of the orbit of a body subject to a central force.

It was first ... more

Tractrix

Tractrix is the curve along which an object moves, under the influence of friction, when pulled on a horizontal plane by a line segment attached to a ... more

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