# proportion

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Related to proportion: Direct proportion

## proportion,

in mathematics, the equality of two ratiosratio.
The ratio of two quantities expressed in terms of the same unit is the fraction that has the first quantity as numerator and the second as denominator. For example, if in a group of 100 people 5 die, the ratio of deaths to the total number in the group is 5/100=1/20=.05.
. Two pairs of quantities a,b and c,d are in proportion if their ratios a/b and c/d are equal, i.e., if the equation a/b=c/d is true. For example, the lengths of two sides of any triangle and the lengths of the corresponding two sides of any similar (same-shaped) triangle are in proportion, for the ratio of the two sides of the first can be proved to be the same as the ratio of the two sides of the second. The proportion a/b=c/d was formerly written a:b::c:d and is read as "a is to b as c is to d." In this form it is customary to call b and c the means and a and d the extremes. These terms are used in the statement of the rule—the product of the means equals the product of the extremes. When the proportion is written in equation form, however, this rule is seen to be simply the result of a familiar algebraic operation. Similarly all the other rules stated for proportions become obvious when the proportion is written as an equation and the usual rules of algebra are applied. The special proportion a/b=b/(a+b) is known as the Divine Proportion, or Golden SectionGolden Section,
in mathematics, division of a line segment into two segments such that the ratio of the original segment to the larger division is equal to the ratio of the larger division to the smaller division.
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## Proportion

The ratio of one part to another, or its relationship to the whole; a comparison of parts as to size, length, width, and depth.
Illustrated Dictionary of Architecture Copyright © 2012, 2002, 1998 by The McGraw-Hill Companies, Inc. All rights reserved
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## Proportion

(1) In mathematics, a proportion is a statement of the equality of two ratios:

The quantities a, b, c, and d are called the terms of the proportion; a and d are the extremes, and b and c are the means. It is a fundamental property of a proportion that the product of the means must equal the product of the extremes: bc = ad. This property is made use of in checking the correctness of a proportion and in expressing one of the terms by means of the others—for example,

(2) In the plastic arts, proportion refers to the relation between the magnitudes of the elements of an artistic work or between the magnitudes of the individual elements and the work as a whole. A distinction is made between systems of proportion used in architecture and systems of proportion used in the depiction of the human body or face. The concept of proportion originated with the architects and artists of antiquity, who used certain modules and geometric constructions in creating their works. Besides systems of proportion based on ratios equal to integers or quotients of integers, systems involving irrational numbers were in wide use. An example is the golden section. Systems of proportion that reflected regularities actually existing in nature were often associated with mythological conceptions of the harmony of the universe. In modern architecture and design, an important problem is the development of systems of proportion under the conditions of the standardization of dimensions and parameters of products.

### REFERENCES

Brunov, N. Proportsii antichnoi i srednevekovoi arkhitektury. [Moscow, 1936.]
Ghyka, M. Estetika proportsii v prirode i iskusstve. Moscow, 1936. (Translated from French.)
Mössel, E. Proportsii v anlichnosti i v srednie veka. Moscow, 1936. (Translated from German.)
Ocherki teorii arkhitekturnoi kompozitsii (collection). Moscow, 1960.
Mikhailov, B. P. Vitruvii i Ellada. Moscow, 1967.
Panofsky, E. “Die Entwicklung der Proportionslehre als Abbild der Stilentwicklung.” Monatshefte für Kunstwissenschaft, 1921, vol. 14, pp. 188–219.
Graf, H. Bibliographie zum Problem der Proportionen. Speyer, 1958.
The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.

## proportion

[prə′pȯr·shən]
(mathematics)
The proportion of two quantities is their ratio.
The statement that two ratios are equal.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

## proportion

1. Maths a relationship that maintains a constant ratio between two variable quantities
2. Maths a relationship between four numbers or quantities in which the ratio of the first pair equals the ratio of the second pair
Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005
References in periodicals archive ?
The golden proportion and RED were not existed between the perceived widths of maxillary anterior teeth.
This ratio is considered to be the Golden Proportion and can be found throughout the world.
Together, from central to canine the proportion must be 1.6:1:0.6 (Ricketts).
In all regions, the proportion of women working in senior roles this year increased from a year earlier: to 13.7% from 11% in North America; to 12.4% from 9.7%; and 11.1% from 10% in the rest of the world.
THE PROPORTION PRINCIPLE: The greater an ingredient's proportion in the formulation, the more its feeder's discharge-rate variability influences the proportions of other ingredients.
Because the mean value of the proportion of the population (15 and older) that is separated is 0.012, or 1.2 percent, we consider the effects of doubling the percent separated to have comparable proportion-based effects from the two relationship statuses.
However, the predominant method varied by region: Sterilization was the most common method in Asia as a whole, as well as in Latin America and the Caribbean; IUDs predominated in eastern, central and western Asia; long-acting hormonal contraceptives (mostly injectables) were the most frequently used methods in Sub-Saharan Africa overall and in southeast Asia; oral contraceptives accounted for the largest proportion of method use in Northern Africa; and barrier methods were the most commonly used contraceptives in middle and western Africa.
Despite the lack of clear variation in the proportions of those unsympathetic to the demonstrations between the different educational levels, the proportion of sympathizers climbs with increasing levels of education, while the proportion of those unable to determine their attitudes decreases.
He said that proportion was less than the proportion of previous year 2018.
'Although female representation at academic meetings has been identified as an important gender equity issue, the proportion of conference speakers who are women has not yet been systematically measured across different medical subspecialties," wrote Shannon M.
Fertilization was performed with 300 kg [ha.sup.-1] of NPK+Zn in the proportion of 08-28-16, and surface fertilization was further applied using 50 kg N [ha.sup.-1].

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