tripling

Tripling is the operation of multiplying a quantity by three. In mathematics, to triple a number means to multiply it by the factor 3, yielding three times the original value. The verb forms include triple, tripled, and tripling used as a noun or gerund. For example, tripling 7 gives 21.

Tripling is a special case of scalar multiplication. For any real number x, tripling yields 3x. It is linear: 3(x + y) = 3x + 3y and 3(ax) = a(3x) for any scalar a. When dealing with units, the result carries the same unit as the original quantity.

Geometrically, tripling a length scales linear dimensions by a factor of 3. Areas scale by 9 (three squared) and volumes by 27 (three cubed). This reflects the general rule that multiplying a dimension by k scales n-dimensional measures by k^n. The concept applies to any comparable quantities, such as time, money, or mass, when units are consistent.

In common usage, "threefold" expresses the same idea: a threefold increase or a value three times as large. In everyday language, one might say "the population tripled" or "the investment tripled in value." The term "tripling" is used across disciplines, including finance, biology, and statistics, to denote a threefold growth.