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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

Normal segment for a given line

The normal segment for a given line is defined to be the line segment drawn from the origin perpendicular to the line. This segment joins the origin with ... more

Margin of error - Effect of population size

The margin of error is a statistic expressing the amount of random sampling error in a survey’s results. The larger the margin of error, the less ... more

Arthur Cayley formula ( regular nonconvex polyhedra)

In geometry, the density of a polytope represents the number of windings of a polytope, particularly a uniform or regular polytope, around its center. ... 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

Triangulation (surveying)

In surveying, triangulation is the process of determining the location of a point by measuring only angles to it from known points at either end of a fixed ... more

Low of sines in spherical triangle

A spherical polygon on the surface of the sphere is defined by a number of great circle arcs which are the intersection of the surface with planes through ... more

Rayleigh Scattering - Intensity of Light

Rayleigh scattering (pronounced /ˈreɪli/ RAY-lee), named after the British physicist Lord Rayleigh (John William Strutt), is the (dominantly) elastic ... more

Alpha helix (rotational angle)

The alpha helix (α-helix) is a common secondary structure of proteins and is a righthand-coiled or spiral conformation (helix). Residues in α-helices ... more

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