Expansions

Expansions are processes or results in which something becomes larger, more extensive, or more detailed. The term is used in several domains to describe different phenomena that share the idea of growth or elaboration. In mathematics, an expansion refers to representing a function or quantity as a series or a more detailed expression. Common examples include the Taylor or Maclaurin expansion, the binomial expansion, and Fourier expansions. Such representations enable approximation, analysis of behavior, and easier computation; they may be finite or infinite, with convergence criteria governing accuracy.

In physics and engineering, expansion describes how physical systems increase in size with temperature or other conditions. Thermal expansion refers to volume or length changes in materials with temperature, quantified by a coefficient of expansion. Cosmology uses expansion to describe the growth of the universe: the scale factor increases over time, leading to redshift and observed recessional velocities, as captured by Hubble’s law.

In business and industry, expansion denotes growth into new markets, products, or capabilities. Firms may pursue geographic expansion, product-line expansion, or capacity expansion, often involving strategy, investment, and organizational changes, along with associated risks and regulatory considerations.

In technology and entertainment, expansion can refer to expansion packs or downloadable content that augments a base product with new features, scenarios, or data, common in video games and software ecosystems.