Search Results for ""

The Steiner triangle DeltaS_AS_BS_C (a term coined here for the first time), is the Cevian triangle of the Steiner point S. It is the polar triangle of the Kiepert parabola. ...

A function tau(n) related to the divisor function sigma_k(n), also sometimes called Ramanujan's tau function. It is defined via the Fourier series of the modular discriminant ...

The area Delta (sometimes also denoted sigma) of a triangle DeltaABC with side lengths a, b, c and corresponding angles A, B, and C is given by Delta = 1/2bcsinA (1) = ...

Consider the average length of a line segment determined by two points picked at random in the interior of an arbitrary triangle Delta(a,b,c) with side lengths a, b, and c. ...

Delta(x_1,...,x_n) = |1 x_1 x_1^2 ... x_1^(n-1); 1 x_2 x_2^2 ... x_2^(n-1); | | | ... |; 1 x_n x_n^2 ... x_n^(n-1)| (1) = product_(i,j; i>j)(x_i-x_j) (2) (Sharpe 1987). For ...

In Homogeneous coordinates (x_1,x_2,x_3), the equation of a circle C is a(x_1^2+x_2^2)+2fx_2x_3+2gx_1x_3+cx_3^2=0. The discriminant of this circle is defined as Delta=|a 0 g; ...

Two elements alpha, beta of a field K, which is an extension field of a field F, are called conjugate (over F) if they are both algebraic over F and have the same minimal ...

A tensor t is said to satisfy the double contraction relation when t_(ij)^m^_t_(ij)^n=delta_(mn). (1) This equation is satisfied by t^^^0 = (2z^^z^^-x^^x^^-y^^y^^)/(sqrt(6)) ...

An elliptic fixed point of a differential equation is a fixed point for which the stability matrix has purely imaginary eigenvalues lambda_+/-=+/-iomega (for omega>0). An ...

The trilinear coordinates alpha:beta:gamma of a point P relative to a reference triangle are proportional to the directed distances a^':b^':c^' from P to the side lines of ...