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A nonzero vector v=(v_0,v_1,...,v_(n-1)) in n-dimensional Lorentzian space R^(1,n-1) is said to be negative timelike if it has imaginary (Lorentzian) norm and if its first ...

A geometric construction, also called a verging construction, which allows the classical geometric construction rules to be bent in order to permit sliding of a marked ruler. ...

Curves with Cartesian equation ay^2=x(x^2-2bx+c) with a>0. The above equation represents the third class of Newton's classification of cubic curves, which Newton divided into ...

If the Gauss map of a complete minimal surface omits a neighborhood of the sphere, then the surface is a plane. This was proven by Osserman (1959). Xavier (1981) subsequently ...

The Ochoa curve is the elliptic curve 3Y^2=2X^3+386X^2+256X-58195, given in Weierstrass form as y^2=x^3-440067x+106074110. The complete set of 23 integer solutions (where ...

An isoptic curve formed from the locus of tangents meeting at right angles. The orthoptic of a parabola is its conic section directrix. The orthoptic of a central conic was ...

A parabola (plural "parabolas"; Gray 1997, p. 45) is the set of all points in the plane equidistant from a given line L (the conic section directrix) and a given point F not ...

The arc length of the parabolic segment y=h(1-(x^2)/(a^2)) (1) illustrated above is given by s = int_(-a)^asqrt(1+y^('2))dx (2) = 2int_0^asqrt(1+y^('2))dx (3) = ...

Two planes that do not intersect are said to be parallel. Two planes specified in Hessian normal form are parallel iff |n_1^^·n_2^^|=1 or n_1^^xn_2^^=0 (Gellert et al. 1989, ...

A path gamma is a continuous mapping gamma:[a,b]|->C^0, where gamma(a) is the initial point, gamma(b) is the final point, and C^0 denotes the space of continuous functions. ...