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The centroid of the four points constituting an orthocentric system is the center of the common nine-point circle (Johnson 1929, p. 249). This fact automatically guarantees ...

The common axis of the three altitude planes of a trihedron.

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 ...

The orthocubic (or ortho cubic) Z(X_4) is a self-isogonal cubic with pivot point at the orthocenter H, so it has parameter x=cosBcosC and trilinear equation (Cundy and Parry ...

An orthogonal basis of vectors is a set of vectors {x_j} that satisfy x_jx_k=C_(jk)delta_(jk) and x^mux_nu=C_nu^mudelta_nu^mu, where C_(jk), C_nu^mu are constants (not ...

Two functions f(x) and g(x) are orthogonal over the interval a<=x<=b with weighting function w(x) if <f(x)|g(x)>=int_a^bf(x)g(x)w(x)dx=0. (1) If, in addition, ...

Orthogonal involution, also called absolute involution, is the involution on the line at infinity that maps orthogonal directions to each other.

In a space E equipped with a symmetric, differential k-form, or Hermitian form, the orthogonal sum is the direct sum of two subspaces V and W, which are mutually orthogonal. ...

Families of surfaces which are mutually orthogonal. Up to three families of surfaces may be orthogonal in three dimensions. The simplest example of three orthogonal surfaces ...