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The upper and lower hinges are descriptive statistics of a set of N data values, where N is of the form N=4n+5 with n=0, 1, 2, .... The hinges are obtained by ordering the ...

The r-Hofstadter triangle of a given triangle DeltaABC is perspective to DeltaABC, and the perspector is called the Hofstadter point. The triangle center function is ...

A clause (i.e., a disjunction of literals) is called a Horn clause if it contains at most one positive literal. Horn clauses are usually written as L_1,...,L_n=>L(=¬L_1 v ... ...

A method for finding roots of a polynomial equation f(x)=0. Now find an equation whose roots are the roots of this equation diminished by r, so (1) The expressions for f(r), ...

For a rectangular hyperbola x = asect (1) y = atant (2) with inversion center at the origin, the inverse curve is x_i = (2kcost)/(a[3-cos(2t)]) (3) y_i = ...

The surface with parametric equations x = (sinhvcos(tauu))/(1+coshucoshv) (1) y = (sinhvsin(tauu))/(1+coshucoshv) (2) z = (coshvsinh(u))/(1+coshucoshv), (3) where tau is the ...

A hyperbolic paraboloid is the quadratic and doubly ruled surface given by the Cartesian equation z=(y^2)/(b^2)-(x^2)/(a^2) (1) (left figure). An alternative form is z=xy (2) ...

The hyperbolic polar sine is a function of an n-dimensional simplex in hyperbolic space. It is analogous to the polar sine of an n-dimensional simplex in elliptic or ...

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 ...

The hyperbolic sine is defined as sinhz=1/2(e^z-e^(-z)). (1) The notation shz is sometimes also used (Gradshteyn and Ryzhik 2000, p. xxix). It is implemented in the Wolfram ...