Formula in the context of "Formulation"

Volume is a measure of regions in three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). The definition of length and height (cubed) is interrelated with volume. The volume of a container is generally understood to be the capacity of the container; i.e., the amount of fluid (gas or liquid) that the container could hold, rather than the amount of space the container itself displaces. By metonymy, the term "volume" sometimes is used to refer to the corresponding region (e.g., bounding volume).

In ancient times, volume was measured using similar-shaped natural containers. Later on, standardized containers were used. Some simple three-dimensional shapes can have their volume easily calculated using arithmetic formulas. Volumes of more complicated shapes can be calculated with integral calculus if a formula exists for the shape's boundary. Zero-, one- and two-dimensional objects have no volume; in four and higher dimensions, an analogous concept to the normal volume is the hypervolume.

The history of mathematical notation covers the introduction, development, and cultural diffusion of mathematical symbols and the conflicts between notational methods that arise during a notation's move to popularity or obsolescence. Mathematical notation comprises the symbols used to write mathematical equations and formulas. Notation generally implies a set of well-defined representations of quantities and symbols operators. The history includes Hindu–Arabic numerals, letters from the Roman, Greek, Hebrew, and German alphabets, and a variety of symbols invented by mathematicians over the past several centuries.

The historical development of mathematical notation can be divided into three stages:

A subscript or superscript is a character (such as a number or letter) that is set slightly below or above the normal line of type, respectively. It is usually smaller than the rest of the text. Subscripts appear at or below the baseline, while superscripts are above. Subscripts and superscripts are often used in formulas, mathematical expressions, and specifications of chemical compounds and isotopes, but have many other uses as well.

In professional typography, subscript and superscript characters are not simply ordinary characters reduced in size; to keep them visually consistent with the rest of the font, typeface designers make them slightly heavier (i.e. medium or bold typography) than a reduced-size character would be. The vertical distance that sub- or superscripted text is moved from the original baseline varies by typeface and by use.

In number theory, a formula for primes is a formula generating the prime numbers, exactly and without exception. Formulas for calculating primes do exist; however, they are computationally very slow. A number of constraints are known, showing what such a "formula" can and cannot be.

Mathematical notation consists of using symbols for representing operations, unspecified numbers, relations, and any other mathematical objects and assembling them into expressions and formulas. Mathematical notation is widely used in mathematics, science, and engineering for representing complex concepts and properties in a concise, unambiguous, and accurate way.

For example, the physicist Albert Einstein's formula ${\displaystyle E=mc^{2}}$ is the quantitative representation in mathematical notation of mass–energy equivalence.

A parity progression ratios (PPR) is a measure commonly used in demography to study fertility. The PPR is simply the proportion of women with a certain number of children who go on to have another child. Calculating the PPR, also known as ${\displaystyle a_{x}}$, can be achieved by using the following formula:

${\displaystyle a_{x}={\text{(women with at least }}x+1{\text{ children ever born) }}/{\text{ (women with at least }}x{\text{ children ever born)}}}$

Snell's law (also known as the Snell–Descartes law, and the law of refraction) is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water, glass, or air.In optics, the law is used in ray tracing to compute the angles of transmission or refraction, and in experimental optics to find the refractive index of a material. The law is also satisfied in meta-materials, which allow light to be bent "backward" at a negative angle of refraction with a negative refractive index. (When light travels from a denser to a rarer medium, the formula is reciprocated (sin r divided by sin i) to find out refractive index)

The law states that, for a given pair of media, the ratio of the sines of angle of incidence ${\displaystyle \left(\theta _{1}\right)}$ and angle of refraction ${\displaystyle \left(\theta _{2}\right)}$ is equal to the refractive index of the second medium with regard to the first (${\displaystyle n_{2,1}}$) which is equal to the ratio of the refractive indices ${\displaystyle \left({\tfrac {n_{2}}{n_{1}}}\right)}$ of the two media, or equivalently, to the ratio of the phase velocities ${\displaystyle \left({\tfrac {v_{1}}{v_{2}}}\right)}$ in the two media.