On the left is asphere, whose volumeV is given by the mathematical formulaV =4/3 πr3. On the right is the compoundisobutane, which has chemical formula (CH3)3CH.
Having obtained this result, the volume of any sphere can be computed as long as its radius is known. Here, notice that the volumeV and the radiusr are expressed as single letters instead of words or phrases. This convention, while less important in a relatively simple formula, means that mathematicians can more quickly manipulate formulas which are larger and more complex.[4] Mathematical formulas are oftenalgebraic,analytical or inclosed form.[5]
In a general context, formulas often represent mathematical models of real world phenomena, and as such can be used to provide solutions (or approximate solutions) to real world problems, with some being more general than others. For example, the formula
is an expression ofNewton's second law, and is applicable to a wide range of physical situations. Other formulas, such as the use of theequation of asine curve to model themovement of the tides in abay, may be created to solve a particular problem. In all cases, however, formulas form the basis for calculations.
Expressions are distinct from formulas in the sense that they don't usually containrelations likeequality (=) orinequality (<). Expressions denote amathematical object, where as formulas denote a statement about mathematical objects.[6][7] This is analogous to natural language, where anoun phrase refers to an object, and a wholesentence refers to a fact. For example, is an expression, while is a formula.
However, in some areas mathematics, and in particular incomputer algebra, formulas are viewed as expressions that can be evaluated totrue orfalse, depending on the values that are given to the variables occurring in the expressions. For example takes the valuefalse ifx is given a value less than 1, and the valuetrue otherwise. (SeeBoolean expression)
Inmodern chemistry, achemical formula is a way of expressing information about the proportions ofatoms that constitute a particularchemical compound, using a single line of chemicalelement symbols,numbers, and sometimes other symbols, such as parentheses, brackets, and plus (+) and minus (−) signs.[9] For example, H2O is the chemical formula forwater, specifying that eachmolecule consists of twohydrogen (H) atoms and oneoxygen (O) atom. Similarly, O− 3 denotes anozone molecule consisting of three oxygen atoms[10] and a netnegative charge.
Thestructural formula forbutane. There are three common non-pictorial types of chemical formulas for this molecule:
theempirical formula C2H5
themolecular formula C4H10 and
thecondensed formula (orsemi-structural formula) CH3CH2CH2CH3.
Inempirical formulas, these proportions begin with a key element and then assign numbers of atoms of the other elements in the compound—as ratios to the key element. For molecular compounds, these ratio numbers can always be expressed as whole numbers. For example, the empirical formula ofethanol may be written C2H6O,[11] because the molecules of ethanol all contain two carbon atoms, six hydrogen atoms, and one oxygen atom. Some types of ionic compounds, however, cannot be written as empirical formulas which contains only the whole numbers. An example isboron carbide, whose formula of CBn is a variable non-whole number ratio, with n ranging from over 4 to more than 6.5.
When the chemical compound of the formula consists of simplemolecules, chemical formulas often employ ways to suggest the structure of the molecule. There are several types of these formulas, includingmolecular formulas andcondensed formulas. A molecular formula enumerates the number of atoms to reflect those in the molecule, so that the molecular formula forglucose is C6H12O6 rather than the glucose empirical formula, which is CH2O. Except for the very simple substances, molecular chemical formulas generally lack needed structural information, and might even be ambiguous in occasions.
Astructural formula is a drawing that shows the location of each atom, and which atoms it binds to.
Incomputing, a formula typically describes acalculation, such as addition, to be performed on one or more variables. A formula is often implicitly provided in the form of acomputer instruction such as.
Degrees Celsius = (5/9)*(Degrees Fahrenheit - 32)
In computerspreadsheet software, a formula indicating how to compute the value of acell, sayA3, could be written as
=A1+A2
whereA1 andA2 refer to other cells (column A, row 1 or 2) within the spreadsheet. This is a shortcut for the "paper" formA3 = A1+A2, whereA3 is, by convention, omitted because the result is always stored in the cell itself, making the stating of the name redundant.
Formulas used in science almost always require a choice of units.[12] Formulas are used to express relationships between various quantities, such as temperature, mass, or charge in physics; supply, profit, or demand in economics; or a wide range of other quantities in other disciplines.
^Stoll, Robert R. (1963).Set Theory and Logic. San Francisco, CA: Dover Publications.ISBN978-0-486-63829-4.{{cite book}}:ISBN / Date incompatibility (help)
