GLOSSARY three-dimensional crystallographic group – toroidal GLOSSARY three-dimensional crystallographic group – toroidal

GLOSSARY three-dimensional crystallographic group – toroidal GLOSSARY three-dimensional crystallographic group – toroidal

torque Turning force. A torque vector is the CROSS PRODUCT of a force vector with the position vector of the point where the force is applied.

torsion

A measure of how a curve turns in space. The torsion of a planar curve is 0.

torus

A closed surface shaped like the surface of a doughnut. The plural is tori.

torus knot A KNOT that can be drawn on the surface of a torus without self- intersections. See also (p, q)- TORUS KNOT .

torus link A LINK that can be drawn on the surface of a torus without self- intersections. total angular deficit Torus The sum of the angular deficits for all the vertices of a

polyhedron. total curvature For an arc of a curve, the total curvature is the net change in

the direction of a unit tangent vector from one endpoint to the other. For example, the total curvature of a semicircle traversed counterclockwise is 180° and the total curvature of a semicircle traversed clockwise is –180°. For a surface, the total curvature is the GAUSSIAN CURVATURE .

total space See FIBER BUNDLE . touch

To be tangent to. trace

The sum of the elements along the main diagonal of a square matrix. tracing puzzle The problem of finding an EULER PATH for a given GRAPH ,

usually one that has an interesting or complex form. track line The actual path a ship or plane travels along. tractrisoid See PSEUDOSPHERE . tractrix The path traced out by a weight on a string being dragged by a

person walking at a constant rate along the x-axis. It is an involute of the catenary. It can be given parametrically by x = a(t – tanh t), y =

a sech t, and it has the x-axis as an asymptote. tractroid The surface formed by rotating a TRACTRIX about its asymptote. train

A series of consecutive circles lying between two nonintersecting circles, one of which contains the other. Each circle in the series is tangent to the two given circles and to one or two other circles in the series.

trajectory The path of an object, usually given by parametric equations.

torque – trajectory GLOSSARY

GLOSSARY

trammel of Archimedes – trapezoid trammel of Archimedes The locus of a point fixed on a segment that slides

with its endpoints fixed on two perpendicular lines. transcendental number An irrational number that cannot be the root of a

polynomial equation with rational coefficients. For example, π is a transcendental number.

transformation

A function that has the properties of both a ONE - TO - ONE FUNCTION and an ONTO FUNCTION .

transformation, method of

A method of solving a problem by solving instead the problem obtained by transforming the givens by an appropriate transformation.

transitive relation

A relation, such as equality or less than, with the property that if a is related to b and b is related to c, then a is related to c.

transitivity class In a tiling, the set of all tiles or vertices equivalent to a

specific tile or vertex of a tiling. translation An ISOMETRY that moves every point in same direction by the

same distance. translation unit

A region whose images under translation will cover a design. translational symmetry Symmetry with respect to TRANSLATION . transpose The matrix formed from a given square matrix A by interchanging

the rows with the columns. It is denoted A T . transposition

A permutation that interchanges two elements.

transvection See SHEAR . transversal

A line intersecting two other lines at distinct points.

transverse axis