# Odd math

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• 09-16-2006
VirtualAce
Odd math
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.
• 09-16-2006
dwks
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.)
• 09-16-2006
VirtualAce
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.
• 09-16-2006
dwks
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. :)
• 09-16-2006
Thantos
Quote:

Originally Posted by Bubba
What is it called when you take a value and perform an operation on it and return the identical value?

Are you referring to an identity?
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.

Quote:

Oddly enough the formulas look to be in the form y=mx+b
Yep the would be. The three major scales are all linear (kelvin and celsius are actually parallel)
• 09-16-2006
laserlight
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.
• 09-16-2006
dwks
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.
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? :)
• 09-17-2006
Thantos
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.
• 09-17-2006
maxorator
Quote:

Originally Posted by dwks
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. :)

US uses Fahrenheit? Wow, I didn't know it before...
• 09-17-2006
VirtualAce
Yeah and inches, quarts, miles per hour, and pounds per foot (instead of newton meters).
• 09-17-2006
siavoshkc
Quote:

What is it called when you take a value and perform an operation on it and return the identical value?
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.

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.
• 09-17-2006
Happy_Reaper
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
• 09-17-2006
Sang-drax
Geometrically, such a value exists if and only if the graphs of the two functions intersect.
• 09-17-2006
Mario F.
You mean the graph and the line intersect, no?

Because a fixed point is calculated from one function only.
• 09-17-2006
twomers
Here's a spreadsheet with a graph of stuff for ya.

Attachment 6785
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