Formula in the context of Begriffsschrift

Formulation is a term used in various senses in various applications, both the material and the abstract or formal. Its fundamental meaning is the putting together of components in appropriate relationships or structures, according to a formula. Etymologically formula is the diminutive of the Latin forma, meaning shape. In that sense a formulation is created according to the standard for the product.

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.

In high-level programming, a variable is an abstract storage or indirection location paired with an associated symbolic name, which contains some known or unknown quantity of data or object referred to as a value; or in simpler terms, a variable is a named container for a particular set of bits or type of data (like integer, float, string, etc...) or undefined. A variable can eventually be associated with or identified by a memory address. The variable name is the usual way to reference the stored value, in addition to referring to the variable itself, depending on the context. This separation of name and content allows the name to be used independently of the exact information it represents. The identifier in computer source code can be bound to a value during run time, and the value of the variable may thus change during the course of program execution.

Variables in programming may not directly correspond to the concept of variables in mathematics. The latter is abstract, having no reference to a physical object such as storage location. The value of a computing variable is not necessarily part of an equation or formula as in mathematics. Furthermore, the variables can also be constants if the value is defined statically. Variables in computer programming are frequently given long names to make them relatively descriptive of their use, whereas variables in mathematics often have terse, one- or two-character names for brevity in transcription and manipulation.

A spreadsheet is a computer application for computation, organization, analysis and storage of data in tabular form. Spreadsheets were developed as computerized analogs of paper accounting worksheets. The program operates on data entered in cells of a table. Each cell may contain either numeric or text data, or the results of formulas that automatically calculate and display a value based on the contents of other cells. The term spreadsheet may also refer to one such electronic document.

In modern spreadsheet applications, several spreadsheets, often known as "worksheets" or simply "sheets", are gathered together to form a "workbook". A workbook is physically represented by a file containing all the data for the book, the sheets, and the cells with the sheets. Worksheets are normally represented by tabs that flip between pages, each one containing one of the sheets, although Numbers changes this model significantly. Cells in a multi-sheet book add the sheet name to their reference, for instance, "Sheet 1!C10". Some systems extend this syntax to allow cell references to different workbooks.

o-Xylene (ortho-xylene) is an aromatic hydrocarbon with the formula C₆H₄(CH₃)₂, with two methyl substituents bonded to adjacent carbon atoms of a benzene ring (the ortho configuration). It is a constitutional isomer of m-xylene and p-xylene, the mixture being called xylene or xylenes. o-Xylene is a colourless slightly oily flammable liquid.

Uvarovite is a chromium-bearing garnet group species with the formula: Ca₃Cr₂(SiO₄)₃. It was discovered in 1832 by Germain Henri Hess who named it after Count Sergei Uvarov (1765–1855), a Russian statesman and amateur mineral collector. It is classified in the ugrandite group alongside the other calcium-bearing garnets andradite and grossular.

Uvarovite is the rarest of the common members of the garnet group, and is the only consistently green garnet species, with an emerald-green color. It occurs as well-formed fine-sized crystals.

The barometric formula is a formula used to model how the air pressure (or air density) changes with altitude.