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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

Oloid Surface Area

An oloid is a three-dimensional curved geometric object that was discovered by Paul Schatz in 1929. It is the convex hull of a skeletal frame made by ... more

Oloid enclosed Volume

An oloid is a three-dimensional curved geometric object that was discovered by Paul Schatz in 1929. It is the convex hull of a skeletal frame made by ... more

Area of an arbitrary triangle (incircle and excircles)

The incircle or inscribed circle of a triangle is the largest circle contained in the triangle; it touches (is tangent to) the three sides. The center of ... more

Length of an arc of a circle (central angle in radians)

Circular arc is a segment of a circle, or of its circumference (boundary) if the circle is considered to be a disc. Central angle is an angle whose apex ... more

Length of an Arc of a Circle

Circular arc is a segment of a circle, or of its circumference (boundary) if the circle is considered to be a disc. Central angle is an angle whose apex ... more

Nose cone ogive shape (radius y at any point x)

Nose cone section of any vehicle or body meant to travel through a compressible fluid medium (such as a rocket or aircraft, missile or bullet) has several ... more

Nose cap Spherically blunted tangent ogive shape ( X-coordinate of the center)

The tangent ogive shape nose-cap is the most familiar in hobby rocketry. The profile of this shape is formed by a segment of a circle such that the rocket ... more

Area of a circular segment

Circular segment is a region of a circle which is “cut off” from the rest of the circle by a secant or a chord. More formally, a circular ... more

Conical pendulum

A conical pendulum is a weight (or bob) fixed on the end of a string (or rod) suspended from a pivot. Its construction is similar to an ordinary pendulum; ... more

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