Hello there,
I'd like very much to hear other readers ideas about what proportionality
really is, and what exactly is their idea about what a
"constant of proportionality"
really is.
For something to think about, proportionality can be depicted even without
a constant such as like this:
y : x
which would mean that x is proportional to y.
Note there is another symbol used for this too, which looks like this:
y ∞ x
except that symbol in the center there looks like that only with an
open end (couldnt find the actual symbol on the list for this board).
Another way to represent this is to use an equation like:
y=K*x
where K is a constant. Because K is a constant it makes y proportional
to x.
Your ideas/comments?
Why bother defining it without "restorting" to writing the K? Like I said overthinking. It just means that any ratiometric change to one will incur the same ratiometric change to the other. Using K instead of english leaves no room for misinterpretation and is much shorter to write.The reason i write this is because this relationship has far reaching consequences
in electronics and other branches of science.
This thing to think about is, when we look at it this way what does this relationship
imply (without resorting to writing the 'K')?
It's just one of the many shorthand symbols involved in math proofs. Why write "K" when you don't have to? especially when you can't define it's actualy value because you don't know what it is? I think you're just overthinking it.
Why bother defining it without "restorting" to writing the K? Like I said overthinking. It just means that any ratiometric change to one will incur the same ratiometric change to the other. Using K instead of english leaves no room for misinterpretation and is much shorter to write.
Why should k be constant for there to be proportionality? If my mortage payment is based on the formula:
I = R*D; where I in the interest, R is the Rate of interest and D is the debt, then the relationship is exactly the definition of proportionality, where I represents Y, D represents X and R represents K. But R isn't necessarily constant. From the start of my loan repayment, R has varied anywhere from 5.5% all the way to 8%.
the current I in a circuit is directly proportional to the potential difference V, and inversely proportional to the resistance R, or I = V/R.
You're mistating Ohm's Law.
Resistance, given by the symbol R, is not the constant of proportionality.
The law stating that the direct current flowing in a conductor is directly proportional to the potential difference between its ends.
You can call it the Sultan of Arabia; that won't make it so. V and R are both varaibles.
You have to know
when 'variables' are really constants and when they are not. Just because R is a
letter like v and i that doesnt automatically make it a variable in an equation.
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