## Friday, August 23, 2013

### -40

-40 Celsius and -40 Fahrenheit are the same.

1. This has always intrigued me. What it says, I guess, is that degrees aren't the same size in the two temperature systems. Otherwise, all values would be the same.

1. Correct. Celsius and Kelvin have that relationship -- that a change of one degree celsius is equal to a change of one degree kelvin, so to convert from one to the other, you simply add a constant (approximately 273 if converting from K to C. Mathematically, one is simply a translation of the other. In my head I view it as the two scales being parallel lines -- though that may not be a useful description for anyone but me.

Celsius was fixed so that zero is water's freezing point and 100 is its boiling point. All else on the celsius scale follows from that. Kelvin was fixed so that zero is absolute zero. I assume that it being a simple translation of celsius was by design. But I don't know the history, so there could be a deeper reason.

Going between fahrenheit and celsius involves both a translation and a dilation (I think that makes it a linear transformation, but I don't remember all the definitions) -- converting from one to the other involves multiplying by a constant and adding a constant. In my head I view the scales as nonparallel lines that cross at -40.

Incidentally, I never use the formulae that we were taught in school. That requires me to remember whether to add or subtract 32, whether to multiply by 5/9 or 9/5 and what order to do those operations. It's easier for me to add 40, multiply by 5/9/ or 9/5 (depending on which direction I am going), and then subtract 40. Because the adding and subtracting of 40 are the same in both directions, all I have to remember is whether to multiply by 5/9 or 9/5. That's a lot less to keep track of. And since going from C to F means increasing the final number (at least in the range of temperatures that I am comfortable in), that means multiplying by 9/5 to go from C to F.

2. I find your formulae better than the ones we learned in school, for the same reason. My spell check does not like the word "formulae".

2. I remember asking my math teacher in 7th grade at what temperature Celsius and Fahrenheit scales were the same. She said they never do.

3. Was that Mrs. Kirsch? She was the one who insisted that if a parking lot had 7 cars, of which 5 were sports cars, then the ratio of sports cars to cars is 5 to 2.