Codimension

Part of speech: noun

Definitions

1. The term refers to the difference in dimensions between a mathematical object and the space it occupies, indicating how many dimensions are missing from a higher-dimensional framework
2. It signifies the count of dimensions that are absent when comparing a mathematical structure with a higher-dimensional space, illustrating the gap in dimensionality
3. A concept in mathematics that describes the number of dimensions that are absent when comparing a given space to a higher-dimensional one

Etymology: "Codimension" is a plain technical compound: the prefix "co-", meaning "together with" or "jointly", attached to "dimension". In mathematics, the codimension of a subspace or object inside a larger space is the number of dimensions it lacks relative to that space. A line inside a plane has codimension one, and a point inside three-dimensional space has codimension three. The "dimension" half traces back to Latin "dimensio," a measuring out, built from "dis-" (apart) and "metiri" (to measure), via Latin "dimensiō" and Old French. The "co-" prefix is the same Latin prefix found in words like "cooperate" and "coexist," and in codimension it works in a complementary sense: the object's dimension and its codimension together make up the dimension of the whole space.