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The surface area of a spherical segment. Call the radius of the sphere R, the upper and lower radii b and a, respectively, and the height of the spherical segment h. The zone ...

Calculus II

The Reuleaux tetrahedron, sometimes also called the spherical tetrahedron, is the three-dimensional solid common to four spheres of equal radius placed so that the center of ...

The hyperbolic cosecant is defined as cschz=1/(sinhz)=2/(e^z-e^(-z)). (1) It is implemented in the Wolfram Language as Csch[z]. It is related to the hyperbolic cotangent ...

The hyperbolic cotangent is defined as cothz=(e^z+e^(-z))/(e^z-e^(-z))=(e^(2z)+1)/(e^(2z)-1). (1) The notation cthz is sometimes also used (Gradshteyn and Ryzhik 2000, p. ...

The hyperbolic secant is defined as sechz = 1/(coshz) (1) = 2/(e^z+e^(-z)), (2) where coshz is the hyperbolic cosine. It is implemented in the Wolfram Language as Sech[z]. On ...

A natural equation is an equation which specifies a curve independent of any choice of coordinates or parameterization. The study of natural equations began with the ...

A spherical segment is the solid defined by cutting a sphere with a pair of parallel planes. It can be thought of as a spherical cap with the top truncated, and so it ...

A branch of mathematics that is a sort of generalization of calculus. Calculus of variations seeks to find the path, curve, surface, etc., for which a given function has a ...

Gaussian curvature, sometimes also called total curvature (Kreyszig 1991, p. 131), is an intrinsic property of a space independent of the coordinate system used to describe ...