formelen

Formelen, or the formula, is a concise symbolic representation used to express a relationship, rule, or calculation. A formula uses variables to denote quantities and constants for fixed values. It can be explicit (non-recursive) or recursive, depending on whether it directly computes a value from inputs or defines a rule that produces subsequent terms.

In mathematics, common examples include the quadratic formula x = [-b ± sqrt(b^2 - 4ac)]/(2a), the area formula A = πr^2, and the Pythagorean theorem a^2 + b^2 = c^2. In algebra, formulas express relationships such as the sum of a geometric series or the slope formula m = (y2 - y1)/(x2 - x1). In calculus, derivative and integral formulas provide rules for rates of change and accumulation.

In physics and engineering, formulas relate physical quantities: F = ma (Newton's second law), E = mc^2, Ohm's law V = IR. In chemistry, chemical formulas represent the composition of substances, e.g., H2O for water or C2H5OH for ethanol, and empirical and molecular formulas convey relative counts of atoms.

Notation and interpretation depend on context and units. Formulas may be used in computations, proofs, or to derive further results. In programming, formulas can be implemented as functions or expressions. The distinction between a formula and an equation is that a formula provides a rule to compute a value, while an equation asserts the equality of two expressions.