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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

Circle equation in polar system

The general equation for a circle with a center not necessary at the pole, gives the length of the radius of the circle.
The polar coordinate system ... more

Area of a Reuleaux triangle

A Reuleaux triangle is a curve of constant width,( the separation of two parallel lines tangent to the curve is independent of their orientation), based ... more

Spirograph (rotation angle of the inner circle)

Spirograph is a geometric drawing toy that produces mathematical roulette curves of the variety technically known as hypotrochoids and epitrochoids.
A ... more

Area of a Torus

In geometry, a torus (pl. tori) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the ... more

Interior Volume of a Torus

In geometry, a torus (pl. tori) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the ... more

Kepler's Second Law

In astronomy, Kepler’s laws of planetary motion are three scientific laws describing the motion of planets around the Sun.

1.The orbit of a ... more

Pressure distribution on a Contact Area between a rigid cylinder and an elastic half-space

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Secant of the sum of three angles

Trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, ... more

Cosecant of the sum of three angles

Trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, ... more

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