A proportion is a mathematical statement expressing equality of two ratios.
<math>a:b=c:d</math>
a and d are called extremes, b and c are called means.
Proportion can be written as <math>\frac{a}{b}=\frac{c}{d}</math>, where ratios are expressed as fractions.
Such a proportion is known as geometrical proportion, not to be confused with arithmetical proportion and harmonic proportion.
Properties of proportions
- Fundamental rule of proportion. This rule is sometimes called Means‐Extremes Property. If the ratios are expressed as fractions, then the same rule can be phrased in terms of the equality of "cross-products"
Harmonic proportion
If the means of the geometric proportion are equal, and the rightmost extreme is equal to the difference between the leftmost extreme and a mean, then such a proportion is called harmonic: <math> a : b = b : (a - b) </math>. In this case the ratio <math> a : b </math> is called golden ratio.
See also
- Ratio
- Proportionality
- Correlation