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Given four points, A, B, C, and H, let H be the orthocenter of DeltaABC. Then A is the orthocenter DeltaHBC, B is the orthocenter of DeltaHAC, and C is the orthocenter of ...

If two pairs of opposite sides of a complete quadrilateral are pairs of perpendicular lines, the quadrilateral is said to be orthocentric. In such a case, the remaining sides ...

One of the operations exists exists (called the existential quantifier) or for all forall (called the universal quantifier, or sometimes, the general quantifier). However, ...

A statistical test making use of the statistical ranks of data points. Examples include the Kolmogorov-Smirnov test and Wilcoxon signed rank test.

Given a polynomial in a single complex variable with complex coefficients p(z)=a_nz^n+a_(n-1)z^(n-1)+...+a_0, the reciprocal polynomial is defined by ...

The root lattice of a semisimple Lie algebra is the discrete lattice generated by the Lie algebra roots in h^*, the dual vector space to the Cartan subalgebra.

A finite set of equations in the same unknowns of which the common solutions have to be determined. Solution of simultaneous equations in implemented in the Wolfram Language ...

A tree G^' whose graph vertices and graph edges form subsets of the graph vertices and graph edges of a given tree G.

An irregular dodecahedron.

f(x)=1-2x^2 for x in [-1,1]. Fixed points occur at x=-1, 1/2, and order 2 fixed points at x=(1+/-sqrt(5))/4. The natural invariant of the map is rho(y)=1/(pisqrt(1-y^2)).