Tree diagram

A diagram consisting of line segments (edges) connected to points (vertices) like the branches and twigs of a tree, **a tree diagram** is used to indicate the relationship between sets or events, for example a family tree.

Tree diagrams can also be used to represent the set of outcomes of a multi-step random experiment, for example, listing the possible outcomes when a coin is tossed twice as shown:

*See also: edge, vertex.*

Trial

A **trial** is any repeatable procedure with a well-defined set of possible outcomes, known as the sample space. An example of a trial would be the flipping of a coin; the sample space would be {H, T}. *See also: probability, sample space.*

Triangular number

A **triangular number** is an element of the set {1, 3, 6, 10, 15 …}. These numbers can be represented as dots that form a triangular array as shown:

*See also: square numbers.*

Trigonometry

Trigonometry is the study of measures related to triangles. Consider the following right-angled triangle, with hypotenuse , right angle, angle *q* and sides (opposite the angle *q* ) and (adjacent to the angle *q* ) as shown:

The relation between the angle *q* and the lengths of the three sides are defined by the trigonometric ratios:

or equivalently:

Similarly, in the following right-angled triangle, with long side length 1 unit, and angle , the vertical side length is and the horizontal side length is :

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If the triangle is dilated by a factor from the point at which the angle is formed, then, by similarity:

with altitude (height) , base , and angle as shown:

*See also: sine, cosine, tangent (trigonometry identity).*

Two-dimensional

An object with width and length is two-dimensional. A polygon is an example of a two-dimensional geometric object. *See also: three-dimensional.*

Two-way table

*See: Karnaugh map.*

U

Undefined term

A term or expression taken as accepted without definition. These are the basic building blocks of mathematics. For example, element and set are undefined terms in *algebra and logic*, while point and line are undefined terms in geometry. Undefined terms may be characterised by informal description or illustrated by examples. Other mathematical terms and expressions are defined using undefined terms and relations on them.

Union (set)

Given two sets *A* and *B*, their **union**, written *A* ∪ *B* is the set of all elements which occur in either set, listed without repetition. For example, if *A* = { *a* , *b* , *d* , *z* } and *B* = { *a* , *c* , *x* , *y* , *z* } then *A* ∪ *B* = { *a* , *b* , *c* , *d* , *x* , *y* , *z* }. *See also: set.*

Unit

A **unit** is a basic or fundamental construct for counting and/or measurement. For example, the number 1 is the unit for counting (from the Latin *unus* for one). The metre is the standard unit for measurement of length in the metric system.

Unit fraction

A unit fraction is a simple fraction whose numerator is 1, that is, a fraction of the form , where is a natural number. For example, is a unit fraction but is not a unit fraction.

*See also: fraction.*

Univariate data

Data relating to measurement of a single variable, for example, shoe size. *See also: data.*

Universal set

The set containing all objects or elements, including itself, within a given context. The complement of the universal set is the empty set.

*See also: complement (set), empty set, set.*

Unplugged

A commonly used term for computational thinking activities carried out without digital technology. “Unplugged” representations of algorithms may include structured mathematical processes, English representations (steps) or flowcharts.

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