formúlur

Formúlur are symbolic expressions used to describe relationships, rules, or calculations in mathematics, science, and related fields. They condense quantities, variables, and constants into compact rules that can be applied to compute unknown values, test propositions, or model phenomena. A formula typically involves variables, mathematical operators, and sometimes constants, and may rely on a specific set of units or dimensions.

Formulas appear in several domains. In mathematics, they express relationships such as area or solutions to equations, for example A = π r² for a circle or the quadratic formula x = (-b ± sqrt(b^2 - 4ac)) / (2a). In physics, formulas relate physical quantities, such as F = ma or E = mc². In chemistry, chemical formulas indicate composition, e.g., H2O for water, and empirical formulas show the simplest whole-number ratio of elements. In statistics and probability, formulas underlie calculations like standard deviation or Bayes’ theorem. In computing and information technology, formulas appear in spreadsheets and programming to compute results from inputs.

Formulas are built from definitions and axioms, and their use often requires attention to units and dimensions to ensure consistency through dimensional analysis. They can be derived from more general principles or stated as rules of thumb for specific applications. In education and research, formulas serve both as tools for calculation and as concise summaries of relationships.

Etymology and usage: the term formula comes from Latin forma, via medieval Latin forma. In Icelandic, formúlur is the plural form of formúla, used across science and mathematics to denote such expressions.