From Wikipedia, the free encyclopedia Formula
Formula
In mathematics, a formula is an entity constructed using In computer spreadsheet software, a formula indicating
the symbols and formation rules of a given logical lan- how to compute the value of a cell, say A3, is written such
guage. In science, a specific formula is a concise way of as
expressing information symbolically as in a mathemat- =A1+A2
ical or chemical formula. The plural of formula can be
spelled either formulae (like the original Latin) for math- where A1 and A2 refer to other cells (column A, row 1 or
ematical or scientific senses, or formulas for more general 2) within the spreadsheet. This is a shortcut for the "pa-
senses.[1] The informal use of the term formula in science per" form A3 = A1+A2 where A3 is, by convention, omitted
refers to the general construct of a relationship between because the result is always stored in the cell itself and
given quantities. would be redundant.
Such formulae are the key to solving an equation with
variables. For example, determining the volume of a Formulae with prescribed units
sphere requires a significant amount of integral calculus;
but, having done this once, mathematicians can produce A physical quantity can be expressed as the product of
a formula to describe the volume in terms of some other a number and a physical unit. A formula expresses a re-
parameter (the radius for example). This particular for- lationship between physical quantities. A necessary con-
mula is: dition for a formula to be valid is that all terms have
the same dimension, meaning every term in the formula
could be potentially converted to contain the identical
unit (or product of identical units).
In the example above, for the volume of a sphere, we
Having obtained this result, and knowing the radius of may wish to compute with r = 2.0 cm, which yields
the sphere in question, we can quickly and easily deter-
mine its volume. Note that the quantities V, the volume,
and r the radius are expressed as single letters. This con-
vention, while less important in a relatively simple for-
mula, means that mathematicians can more quickly ma- There is vast educational training about retaining units
nipulate larger and more complex formulae. in computations, and converting units to a desirable
Expressions are distinct from formulae in that they form, such as in units conversion by factor-label.
cannot contain an equals sign; whereas formulae are However, the vast majority of computations with
comparable to sentences, expressions are more like measurements are done in computer programs with no
phrases. facility for retaining a symbolic computation of the units.
In a general context, formulae are applied to provide Only the numerical quantity is used in the computation.
a mathematical solution for real world problems. Some This requires that the universal formula be converted
may be general: F = ma, which is one expression of New-
a to a formula that is intended to be used only with pre-
ton’s second law, is applicable to a wide range of physical scribed units, meaning the numerical quantity is implic-
situations. Other formulae may be specially created to itly assumed to be multiplying a particular unit. The re-
solve a particular problem; for example, using the equa- quirements about the prescribed units must be given to
tion of a sine curve to model the movement of the tides users of the input and the output of the formula.
in a bay. In all cases however, formulae form the basis for For example suppose the formula is to require that
all calculations. , where tbsp is the U.S. table-
spoon (as seen in conversion of units) and VOL is the
In computing name for the number used by the computer. Similarly,
the formula is to require . The de-
In computing, a formula typically describes a calculation, rivation of the formula proceeds as:
such as addition, to be performed on one or more vari-
ables. A formula is often implicitly provided in the form
of a computer instruction such as.
Degrees Celsius = (5/9)*(Degrees Fahrenheit -32)
1
From Wikipedia, the free encyclopedia Formula
apparent in the impossibility to derive a formula with
Given that , the formula
prescribed units. It would not be possible to derive a for-
with prescribed units is
mula consisting only of numbers and dimensionless ra-
tios.
The formula is not complete without words such as: "VOL
is volume in tbsp and RAD is radius in cm Other possible
cm". References
words are "VOL is the ratio of V to tbsp and RAD is the ra- [1] Oxford Dictionaries: formula.
cm."
tio of r to cm
The formula with prescribed units could also appear
with simple symbols, perhaps even the identical symbols See also
as in the original dimensional formula: • Mathematical notation
• Formula (mathematical logic)
• Spreadsheet
and the accompanying words could be: "where V is vol-
ume (tbsp and r is radius (cm
tbsp) cm)".
If the physical formula is not dimensionally homoge-
External links
neous, and therefore erroneous, the falsehood becomes • Formula Wikitionary
Retrieved from "http://en.wikipedia.org/w/index.php?title=Formula&oldid=464664869"
Categories:
• Mathematical notation
This page was last modified on 7 December 2011 at 23:53. Text is available under the Creative Commons Attribution-
ShareAlike License; additional terms may apply. See Terms of use for details. Wikipedia® is a registered trademark of
the Wikimedia Foundation, Inc., a non-profit organization.Contact us
Privacy policy About Wikipedia Disclaimers
2