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I'm trying to create an app for a workshop that I'll be running.

It's going to be a variation of the temperature converter app that tends to be the "Introduction to programming" default.

Anyway, I was wondering about conversions.

If you take, temperature, time, pressure, distance... and the rest of the categories from this site... http://www.digitaldutch.com/unitconverter/electric_current.htm

Do all the conversions follow the pattern...

y = mx + c (i.e. the formula of a straight line).

Can you give me an example that doesn't use this calculation? I can't think of one. In fact, with the exception of fahrenheit, most of them are just y = mx. Oh and Celsius to Kelvin is just a y = x + c.

Is that correct?

Fogmeister
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The reason you see the pattern you do: y = mx + c, is because

  • in many cases, there is a precise conversion factor m being used, along with adjustment of a constant c, where needed (as in Fahrenheit-Celsius conversions). E.g., this is the case in degrees to radians, feet-yards, min-hours, etc.

  • or else an approximation of a conversion factor (m) is being used (especially between systems) - an approximation to however many significant figures for increasing accuracy. E.g., pounds-kilograms, feet-meters.

See, e.g., the National Institute of Standards and Technology's website for such approximating factors, and the conversion processes you observe.

amWhy
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I can't think of one off the top of my head, but if you can imagine having square degrees Fahrenheit...

$$F^2 = \left( \frac{9}{5} C + 32 \right)^2$$

...then technically you would have a quadratic relationship.

The thing is, as you noted, most of the examples you found were of the form $y = mx$. This means that, in higher dimensions you would just have $y^n = (mx)^n = m^n x^n = cx^n$ ($c$ constant), which is a linear relationship with respect to $y^n$ and $x^n$ (e.g. square miles and square kilometers). Hence, higher dimensional versions of most units won't help.

But why should one dimensional quantities like metres and kilograms even have a relationship of the form $y=mx$ with miles and pounds? Well I'm guessing here, but imagine I had to measure a road, but all I had was a stick. Then the answer I get would be some number of stick-lengths and, if I had a different stick, I'd get a different answer. But I could always convert from one to the other using a linear function, and it would be something based on the ratio between the stick-lengths.

And why should there be no constant term? Well, both ways of measuring the road would agree at one point - at zero. If I had no distance to measure, I'd need no stick-lengths. This agreement point at $(0, 0)$ guarantees a function of the form $y=mx$. In the case of Fahrenheit/Celcius, no such intuitive zero point was possible, giving it the constant term of 32 degrees.

That's only if you work intuitively though. You could always define log-metres or something to get an unusual relationship...

Sp3000
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  • Thanks, yeah I was thinking of the same thing. Your stick analogy is better than what I had come up with though. I also though of log scales. I don't know if a linear scale for earthquake strength exists but if it did you can't use y = mx + c to convert to the Richter scale. – Fogmeister Jun 17 '13 at 16:33
  • Now that you've mentioned it I just tried looking (decibels, pH, etc. as well) but I guess it's because of the nature of what's being measured that it always seems to be logarithmic there too... – Sp3000 Jun 17 '13 at 16:38