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The three planes determined by the edges of a trihedron and the internal bisectors of the respectively opposite faces are coaxal, and the common line of these planes is ...

A convex set K is centro-symmetric, sometimes also called centrally symmetric, if it has a center p that bisects every chord of K through p.

Let P=alpha_1:beta_1:gamma_1 and Q=alpha_2:beta_2:gamma_2 be points, neither of which lie on a sideline of the reference triangle DeltaABC. The P-Ceva conjugate X of Q is ...

Suppose P=p:q:r and U=u:v:w are points, neither lying on a sideline of DeltaABC. Then the cevapoint of P and U is the point (pv+qu)(pw+ru):(qw+rv)(qu+pv) :(ru+pw)(rv+qw).

A Cevian point P is point with respect to which a set of Cevians of a triangle are taken. Connecting the endpoints of the Cevians through a point P gives the so-called Cevian ...

Vandeghen's (1965) name for the transformation taking points to their isotomic conjugates.

Chained arrow notation is a notation which generalizes the Knuth up-arrow notation and is defined as a^...^b_()_(c)=a->b->c.

A sequence of circles which closes (such as a Steiner chain or the circles inscribed in the arbelos) is called a chain.

A surface with tetrahedral symmetry which looks like an inflatable chair from the 1970s. It is given by the implicit equation The surface illustrated above has k=5, a=0.95, ...

The partial differential equation u_(xx)+(y^2)/(1-(y^2)/(c^2))u_(yy)+yu_y=0.