truncations

Truncation is the act of shortening something by removing part of it. The term appears across disciplines, often referring to removing material, shortening signals, or limiting observed data. Different fields use the word with domain-specific meanings.

In geometry and polyhedral construction, truncation is an operation that slices off the vertices of a polyhedron, replacing each with a new face. The extent of truncation determines the size of the new faces. Known examples include the truncated tetrahedron and the truncated icosahedron, also called the soccer-ball shape.

In linguistics and text processing, truncation shortens a word or phrase by cutting off part of it. Examples include info from information and ad from advertisement. Truncation produces abbreviations and is common in informal writing, headlines, and data-entry systems that require fixed-length fields.

In computing and databases, truncation refers to reducing width or precision. Strings may be truncated to a maximum length; numerical values can be truncated when casting types. In SQL, TRUNCATE TABLE quickly removes all rows from a table, often resetting identity counters, and differs from DELETE.

In statistics, truncation occurs when observed data are restricted to a subrange, producing a truncated distribution such as a truncated normal. Left-truncated or right-truncated data affect estimation and inference, because the missing portions carry information about the underlying population.

In numerical analysis, truncation also refers to omitting higher-order terms in a series or approximation, generating truncation error that bounds the difference between the approximate and exact result.