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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

Spirograph (Y-coordinate of the traiectory of the pen-hole in the inner disk of a Spirograph)

Spirograph is a geometric drawing toy that produces mathematical roulette curves as hypotrochoids and epitrochoids. A fixed outer circle of radius R is ... more

Spirograph (X-coordinate of the traiectory of the pen-hole in the inner disk of a Spirograph)

Spirograph is a geometric drawing toy that produces mathematical roulette curves as hypotrochoids and epitrochoids. A fixed outer circle of radius R is ... more

Hyperbolic triangle ( length of the base)

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

Hyperbolic triangle ( length of the altitude)

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

Wing loading - turning radius

In aerodynamics, wing loading is the total weight of an aircraft divided by the area of its wing. The stalling speed of an aircraft in straight, level ... 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

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

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

Flattening - 1st variant

Flattening is a measure of the compression of a circle or sphere along a diameter to form an ellipse or an ellipsoid of revolution (spheroid) respectively. ... more

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