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What is it called when you take a value and perform an operation on it and return the identical value?
The formula to convert Celsius to Fahrenheit is
F=(9/5C)+32
Vice versa is:
C=(F-32)(5/9)
If you use the value -40, you get the same result. 9/5 is 1.8 in decimal
1.8*(-40)+32 = -40
(-40-32)(1.8)=-40
I dunno why this works out this way and would be interested for someone to explain how and why it does.
It's called an intersection, I think. You can see the result quite nicely in a graphing calculator. You enter in the two formulae; each will be a line of different slope. The point at which the lines intersect is the point where what you mentioned is true. (Sorry if you already know this, which I'm sure you do.)
Well I know what an intersection is, but I guess it never dawned on me. It sure would have saved me at work where I thought people were not putting in enough antifreeze to reach -40C. After a bit of testing we realized that the two temps were the same.
Oddly enough the formulas look to be in the form y=mx+b.
Living in a country that's so close to the US but uses Celsius (ie Canada) means that you have to be familiar with those things. :)
Are you referring to an identity?Quote:
Originally Posted by Bubba
Though those aren't normally defined for a specific value, but instead all allowed values.
The intersection would give you the point where it wouldn't matter which formula you used, not which value would return that same value.
Yep the would be. The three major scales are all linear (kelvin and celsius are actually parallel)Quote:
Oddly enough the formulas look to be in the form y=mx+b
Yeah, I remember this from playing the trivia game MindTrap. When I had to do a programming assignment in university recently (I am learning Java as a first year university student, fortunately or unfortunately), one of the first things I did to test was to try out -40.
It also gives the point at which the functions have the same value, because if it doesn't matter which one you use, they must be the same, must they not? :)Quote:
The intersection would give you the point where it wouldn't matter which formula you used, not which value would return that same value.
Yes the intersection would give you the same value regardless of the equation used, but thats not what I said.
The intersection of two linear equations does not guartnee that f(x) = x, it only tells you that f(x) = y = g(x). I'd be willing to stipulate that for the majority of functions no such value exists, though I suppose that having the two functions be inverses of each other my play a part in it.
US uses Fahrenheit? Wow, I didn't know it before...Quote:
Originally Posted by dwks
Yeah and inches, quarts, miles per hour, and pounds per foot (instead of newton meters).
Any function can have one or more values in its domination that is maped to the same value in its range. There is a special function that maps all values to themselves f(x)=x. It has a special name, but I don't know what it is in English.Quote:
What is it called when you take a value and perform an operation on it and return the identical value?
You know that
F=(9/5C)+32 is as same as C=(F-32)(5/9), they are the same equations.
And because it is a linear equation, one x is only maped to one F(x) so it can be inverted esily as we do.
A value x such that f(x) = x for a function f is called a fixed point.
In this sense, you could say -40 if a fixed point of the funtion F = (9/5)C + 32.
That link gives a somewhat broad definition of a fixed point. Here's another one that's not too bad, but a little bit more clear :
http://en.wikipedia.org/wiki/Fixed_p...mathematics%29
Geometrically, such a value exists if and only if the graphs of the two functions intersect.
You mean the graph and the line intersect, no?
Because a fixed point is calculated from one function only.
Here's a spreadsheet with a graph of stuff for ya.
Attachment 6785
I think what Bubba was referring was to Happy_Reaper's reply. Fixed points, not intersections.
It is obvious that both functions intersect at the fixed point since both functions cancel each other.Quote:
Originally Posted by Bubba
I wish you people would stop being so stuck-up and switch to metric. :pQuote:
Originally Posted by Bubba
>> I wish you people would stop being so stuck-up and switch to metric.
Heh. I agree .... what was that quote ...
Grandpa Simpson: The Metric System is the tool of the devil! My car gets five rods to the hog's head and that's the way I likes it!
:p
BTW, there are worse things than pounds per square inch in mech eng!!
This always happens whenever you have a linear relationship of the form f(x) = mx + b, where m != 1. You'll find that f(x) = x when x = b/(1-m).
What you have are two linear functions that are inverses of each other (by design, since converting from Fahrenheit to Celcius to Fahrenheit should give you the same temperature), and since one has a fixed point, the inverse must have the same fixed point.
You'll find the same thing with, say, g(x) = 2x + 3 and h(x) = (1/2)(x-3).
Every non-constant linear function has an inverse function, and they'll always have the same effect.