Concept
Proportionality (mathematics)
Overview
In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio. The ratio is called coefficient of proportionality (or proportionality constant) and its reciprocal is known as constant of normalization (or normalizing constant). Two sequences are inversely proportional if corresponding elements have a constant product.
Two functions
f
(
x
)
{\displaystyle f(x)}
and
g
(
x
)
{\displaystyle g(x)}
are proportional if their ratio
f
(
x
)
g
(
x
)
{\textstyle {\frac {f(x)}{g(x)}}}
is a constant function.
If several pairs of variables share the same direct proportionality constant, the equation expressing the equality of these ratios is called a proportion, e.g., a/b = x/y = ⋯ = k (for details see Ratio).
Proportionality is closely related to linearity.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
In the original texts
Passages from public-domain books where Proportionality (mathematics) is discussed.
The recognition, therefore, of any such law of proportionality is superseded by the more comprehensive principle, in which as much of it as is true is implicitly asserted.(134)
John Stuart Mill, A System of Logic, Ratiocinative and Inductive
states what it is; names the idea
Two sets of four points each are defined as having the same anharmonic ratio, when (1) each set of four lies in one straight line, and (2) corresponding points of different sets lie two by two on four straight lines through a single point, or when both sets have this relation to any third set[123]. And reciprocally: Two sets of four straight lines are defined as having the same anharmonic ratio when (1) each set of…
Bertrand Russell, An essay on the foundations of geometry
states what it is
Mathematicians have distinguished different degrees of continuity, and have confined the word "continuous," for technical purposes, to series having a certain high degree of continuity. But for philosophical purposes, all that is important in continuity is introduced by the lowest degree of continuity, which is called "compactness." A series is called "compact" when no two terms are consecutive, but between any two…
Bertrand Russell, Our Knowledge of the External World as a Field for Scientific Method in Philosophy
states what it is
Such a resultant force, as it is called, may be found for any pair of forces throughout the group. Similarly, for any pair of such resultants a single resultant may be found. And by repeating this course, all of them may be reduced to two. If these two are equal and opposite—that is, if there is no line of greatest traction, motion does not take place.
Herbert Spencer, First Principles
states what it is
Because in these phenomena there is something very small. The simple law observed, then, is only a result of the general analytical rule that the infinitely small increment of a function is proportional to the increment of the variable. As in reality our increments are not infinitely small, but very small, the law of proportionality is only approximate, and the simplicity is only apparent. What I have just said…
Henri Poincaré, The Foundations of Science
states what it is; names the idea
Philosophers who discussed Proportionality (mathematics)
Related ideas
- Function (mathematics)
- Mathematics
- Mass
- Speed
- Time
- Variable (mathematics)
- Circle
- Diameter
- Ratio
- Equivalence relation
Place in the tradition
Part of History of philosophy in Poland.
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