# Talk:Proportionality (mathematics)

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## (Does linear imply proportional?)

If y = kx + c, then would it not be correct to say that y is proportional to x, or y is directly proportional to x irrespective whether or not c = 0 or non-zero?
—Preceding unsigned comment added by 203.97.78.203 (talk) 00:02, 10 June 2005

I'm pretty sure it is. I was just about to comment on that issue.
—Preceding unsigned comment added by 63.194.211.181 (talk) 04:41, 23 August 2005 (two edits)
I don't think so. Their change is proportional, but they are not themselves.
--Patrick 12:44, 23 August 2005 (UTC)
No, they're not proportional unless c = 0.
--198.59.188.232 02:44, 24 October 2005 (UTC)

## Direct proportionality

There is no distinction made between merely proportional and directly proportional, in the article. Perhaps one could be made by commenting on the origin graphically.00:36, 1 November 2003 (UTC)

## what is the symbol for inverse?

the article shows that the symbol for directly proportional is α (alpha), but it doesn't say what the symbol for inverse proportional is. can anyone share that with me, i am having trouble remmebering it. I think its either a backwards alpha or an alpha with a line over or under it, something like that. can anyone help?--68.249.39.158 18:18, 14 February 2006 (UTC)

I thought it was just written as "x is proportional to the reciprocal of y", like this: X α 1/Y capitalist 03:41, 15 February 2006 (UTC)
The sign of proportionality is not the greek lower case letter alpha (α), but the symbol ∝ (in Arial Unicode MS the symbol is a bit too small, in most type faces it is bigger, as seen in LaTeX: ${\displaystyle \propto }$). In some countries, Sweden for instance, the symbol ${\displaystyle \sim }$ or ∼ is used instead of ∝. The Unicode-code for ∝ is U+221D (Proportional to) and for ∼ U+223C (Tilde operator). /85.197.143.234 21:51, 27 May 2006 (UTC)

### Even more symbols

So there is no difference in ∝ and ∼? While checking the Mathematical Operators table at http://www.decodeunicode.org/w3.php?ucHex=2200 i found the character by the name reversed tilde - maybe this is the inverse proportional sign? By the way, there are many more abstruse characters found in this part of Unicode with most of them hardly to figure out. Maybe someone can help out and expand (that is create redirects) for these characters? Thanks, --Abdull 21:29, 28 May 2006 (UTC)

## Graphs

Graphs would be helpful here, for examples of an inverse direct and an inverse square relationship. I don't have an SVG editor, so the only thing I can provide is a PNG... Titoxd(?!?) 07:43, 25 June 2006 (UTC)

## Proportionality to x^2?

Should there be a section on proportionality of x^n (n=1,2,3....)? --124.217.57.41 13:19, 4 September 2007 (UTC)BY Mr. Ignacio

That is not, to my knowledge, proportionality. I suppose you could call that "parabolic proportionality", but that would be original research if not a neogolism.  dmyersturnbull talk 05:15, 3 May 2010 (UTC)

## Improving article

Some suggestions for improving this article include having separate articles for direct and inverse proportion, as they are sufficiently comprehensive and practical topics that deserve separate articles (the redirects will have to be fixed. I must say that I am surprised this article and also ratio are quite short, given their usefulness in real life. I will try to expand the articles once I find the time. I encourage others to help ! Thanks. MP (talkcontribs) 19:20, 19 April 2008 (UTC)

Given the ubiquity of direct proportion in civilization's systems of rationality, one might expect that that cousin "inverse proportion" would get some attention too. But once you look for sources and experts, books and articles, and real instantiation, the subject slips away into obscurity. Presently I am madly attempting to provide references for the article hyperbolic coordinates which is linked from the paragraph that we have presently. Probably the best evidence for obscurity comes from special relativity, where the hyperbolic curve of inverse proportion is taken for a map of the potential future moment, depending on the speed (or rapidity). The decades it has taken experts to expose the underlying linear algebra of Lorentz' transformations reflects the delicacy of parsing a physical model. Please, yes, if you have some references to build an article, that would be of great assistance.Rgdboer (talk) 20:45, 19 April 2008 (UTC)

In addition, the section Symbols mentions two Unicode proportionality symbols, and , but doesn't make any attempt to explain what these symbols are used for, other than giving their Unicode names. There should be a better definition of what each means, over and above the Unicode names. For example, the former of the two is simply named 'PROPORTION', which isn't enough to truly define it.. --Ge0nk (talk) 23:45, 28 August 2013 (UTC)

Two quantities can be directly proportional even if they don't vary by a constant multiple. For example, Newton's law of universal gravitation states that every particle in the universe attracts every other massive particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them[1] This statement can be represented as[2]

${\displaystyle F=G{\frac {m_{1}m_{2}}{r^{2}}}}$,

where:

• F is the gravitational force between the two point masses,
• λ is the gravitational constant,
• m is the first mass,
• m′ is the second mass, and
• r is the distance between m and m′

You can find that in about any physics textbook, even a modern one. Because F depends on three variables, m, m′, and r, F does not vary with m⋅m′ by a constant multiple. Yet, they are proportional. Wolfram Mathworld states[3] "If a is (directly) proportional to b, then a/b is a constant. The relationship is written a proportional b, which implies a=cb for some constant c known as the constant of proportionality. What is a good way to explain that other variables may be involved? We could simply say that ab does not imply that the only variables involved are a and b, but that is awkward. We need a citation for the definition. I've been looking for one but have had little luck. I'll improve the wording a bit.  dmyersturnbull talk 02:28, 3 May 2010 (UTC)

You're just confused by having seen too many examples where the inherent requirement that there are no other variables than the two (i.e., that all other variables are held constant) was not made explicit. In fact, it is implicit that distance be held constant for the first proportionality, and that the product of the masses be held constant for the second.
--Jerzyt 05:55, 30 September 2010 (UTC)

### References

1. ^ Newton, Isaac. Principia Mathematica.
2. ^ Alonso, Marcelo; Edward J. Finn (1970). Physics. Menlo Park, California: Addison-Wesley. p. 306.
3. ^ Weisstein, Eric. "Proportional".

i removed
or equivalently if they have a constant ratio
bcz ratio implies same units, yet for constant speed, distance and time are directly proportional despite different units, and i rem'd
Proportion also refers to the equality of two ratios.
bcz a ratio is a quantity, making the statement redundant and inviting confusion about how it could be useful. (If you have some point, show us on this talk page an example of why anyone would care; if you're right, someone will find a less mysterious way to say it.)

--Jerzyt 06:20, 30 September 2010 (UTC)

## Please emphasize direct proportionality can be negative!

Since there NO charts showing negative slopes, some beginning readers might incorrectly think that direct means positive and inverse means negative.

And the examples in the inverse section also involve a negative proportion, so again, we might mislead people that don't read very closely.

Waxmop (talk) 18:36, 1 December 2013 (UTC)

## ∺

occurrences of ∺ are required for is redirected to this page.   <STyx @ (I promote Geolocation) 16:13, 1 February 2016 (UTC)

Done. Petr Matas 00:23, 3 September 2016 (UTC)

## removed section cleanup

I removed the following part which was party full of format issues but also some of detailed content seem somewhat inappropriate here. It might be ok for its own article though.--Kmhkmh (talk) 09:58, 20 July 2016 (UTC)

### Theorem of Joint Variation

If x ∝ y when z is constant and x ∝ z when y is constant, then x ∝ yz when both y and z vary.


Proof: Since x ∝ y when z is constant Therefore x = ky where k = constant of variation and is independent to the changes of x and y.

Again, x ∝ z when y is constant.

or, ky ∝ z when y is constant (since, x = ky).

or, k ∝ z (y is constant).

or, k = mz where m is a constant which is independent to the changes of k and z.

Now, the value of k is independent to the changes of x and y. Hence, the value of m is independent to the changes of x, y and z.

Therefore x = ky = myz (since, k = mz)

where m is a constant whose value does not depend on x, y and z.

Therefore x ∝ yz when both y and z vary.

Note: (i) The above theorem can be extended for a longer number of variables. For example, if A ∝ B when C and D are constants, A ∝ C when B and D are constants and A ∝ D when B and C are constants, thee A ∝ BCD when B, C and D all vary.

(ii) If x ∝ y when z is constant and x ∝ 1/Z when y is constant, then x ∝ y when both y and z vary.

Some Useful Results:

Theorem of Joint Variation

(i) If A ∝ B, then B ∝ A.

(ii) If A ∝ B and B∝ C, then A ∝ C.

(iii) If A ∝ B, then Ab ∝ Bm where m is a constant.

(iv) If A ∝ BC, then B ∝ A/C and C ∝ A/B.

(v) If A ∝ C and B ∝ C, then A + B ∝ C and AB ∝ C2

(vi) If A ∝ B and C ∝ D, then AC ∝ BD and A/C ∝ B/D

Now we are going to proof the useful results with step-by-step detailed explanation

Proof: (i) If A ∝ B, then B ∝ A.

Since, A ∝ B Therefore A = kB, where k = constant.

or, B = 1/K ∙ A Therefore B ∝ A. (since,1/K = constant)

Proof: (ii) If A ∝ B and B ∝ C, then A ∝ C.

Since, A ∝ B Therefore A = mB where, m = constant

Again, B ∝ C Therefore B = nC where n= constant.

Therefore A= mB = mnC = kC where k = mn = constant, as m and n are both Constants.

Therefore A ∝ C.

Proof: (iii) If A ∝ B, then Ab ∝ Bm where m is a constant.

Since A ∝ B Therefore A = kB where k= constant.

Am = KmBm = n ∙ Bm where n = km = constant, as k and m are both constants.

Therefore Am ∝ Bm.

Results (iv), (v) and (vi) can be deduced by similar procedure.

## Logarithmic proportionality

The current logarithmic proportionality definition

${\displaystyle y=k\log _{a}x}$

is not good, because it can be written as ${\displaystyle y=\log _{a'}x}$, where ${\displaystyle a'={\sqrt[{k}]{a}}}$. The constant k is clearly superfluous because it can be absorbed into the base a′. Furthermore, if x is exponentially proportional to y according to ${\displaystyle x=ka^{y}}$ with ${\displaystyle k\neq 1}$, then y will NOT be logarithmically proportional to x, which is not nice.

I think that the logarithmic proportionality definition should be changed to

${\displaystyle y=c+\log _{a}x.}$

This will correspond to the exponential proportionality defined with ${\displaystyle x=ka^{y}}$, where ${\displaystyle k=a^{-c}}$. Also, y will be logarithmically proportional to x precisely if x is exponentially proportional to y.

Anyway, a reliable source is really needed for this section. Petr Matas 02:34, 3 September 2016 (UTC)