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For a curve with radius vector r(t), the unit tangent vector T^^(t) is defined by T^^(t) = (r^.)/(|r^.|) (1) = (r^.)/(s^.) (2) = (dr)/(ds), (3) where t is a parameterization ...

A tetradecahedron is a 14-sided polyhedron, sometimes called a tetrakaidecahedron. Examples are illustrated above and summarized in the following table. name family augmented ...

The Thomson cubic Z(X_2) of a triangle DeltaABC is the locus the centers of circumconics whose normals at the vertices are concurrent. It is a self-isogonal cubic with pivot ...

A geometric implement discovered in a 19th century book, and whose inventor is unknown. It essentially consists of a semicircle, a segment SR which prolongs its diameter and ...

A tetrahedron having a trihedron all of the face angles of which are right angles. The face opposite the vertex of the right angles is called the base. If the edge lengths ...

There exist points A^', B^', and C^' on segments BC, CA, and AB of a triangle, respectively, such that A^'C+CB^'=B^'A+AC^'=C^'B+BA^' (1) and the lines AA^', BB^', CC^' ...

Consider two directly similar triangles DeltaA_1B_1C_1 and DeltaA_2B_2C_2 with B_1C_1:A_1C_1:A_1B_1=B_2C_2:A_2C_2:A_2B_2=a:b:c. Then a·A_1A_2, b·B_1B_2 and c·C_1C_2 form the ...

In Minkowski space, a twistor may be defined as a pair consisting of a spinor field and a complex conjugate spinor field satisfying the twistor equation.

For a given point lattice, some number of points will be within distance d of the origin. A Waterman polyhedron is the convex hull of these points. A progression of Waterman ...

The Weingarten equations express the derivatives of the normal vector to a surface using derivatives of the position vector. Let x:U->R^3 be a regular patch, then the shape ...