Proportionality Definition and 6 Discussions

In mathematics, two varying quantities are said to be in a relation of proportionality,
multiplicatively connected to a constant; that is, when either their ratio or their product yields a constant. The value of this constant is called the coefficient of proportionality or proportionality constant.

If the ratio (y/x) of two variables (x and y) is equal to a constant (k = y/x), then the variable in the numerator of the ratio (y) can be product of the other variable and the constant (y = k ⋅ x). In this case y is said to be directly proportional to x with proportionality constant k. Equivalently one may write x = 1/k ⋅ y; that is, x is directly proportional to y with proportionality constant 1/k (= x/y). If the term proportional is connected to two variables without further qualification, generally direct proportionality can be assumed.
If the product of two variables (x ⋅ y) is equal to a constant (k = x ⋅ y), then the two are said to be inversely proportional to each other with the proportionality constant k. Equivalently, both variables are directly proportional to the reciprocal of the respective other with proportionality constant k (x = k ⋅ 1/y and y = k ⋅ 1/x).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).

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    B What is the link between proportion and multiplication?

    I found this quote online: “Multiplication is the mathematical manifestation of the fundamental physical phenomenon of proportionality (as addition is to combination).” Question 1: How are multiplication and proportion linked? How can and WHY DOES multiplication model proportion? (My...
  2. ayans2495

    Inverse-Square Law of Radiation

  3. O

    Rotational Movement of a Disc

    I am doing a project, but am struggling to find relationships of proportionality or formulae between my dependent variables (angular velocity, displacement, acceleration of the disc and kinetic energy of the system) and my independent variables (falling masses and then the number of winds) or...
  4. jxj

    Help with proportionality and literal equations

    Homework Statement Its a series of problems essentially basically asking questions about solving proportionality . For example "Hooke's Law of a spring can be described by the equation F = -kx, where F is the force exerted by a spring, K us the spring constant, and X is the amount of distance...
  5. R

    How do proportional relationships derive physics equations?

    in particular f=Gm1m2/r^2?sorry if my question sounds very irrelevant.if f is proportional to m1m2 it implies f=some constant times the same time f is inversely proportional to r^2 .so force = some other constant times 1/r^2.okay.but in most places i see that what is done is they...
  6. S

    Proportionality Constants

    I wanted to ask how are the values of proportionality constants in physical relations determined. How do we come to know their exact values ? An explanation with an example please...