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Claudio L. · 04-01-2016, 06:22 PM

(04-01-2016 05:48 PM)Han Wrote:
(04-01-2016 05:33 PM)Helix Wrote: Why?
For me, 10°+10°+10° = 3x10° = 30°, and 30°/3 = 10°.
I think that an angle multiplied or divided by a constant (a real number) should be an angle.

My guess would be ambiguity in interpreting the real number -- is it a constant multiplier, or did the user intentionally leave off the ° but still wanted to actually have degrees. In the former, you have what is essentially the same as your examples; in the latter, you would be looking at fractions of a circle (as one possible interpretation). With addition, there is only one reasonable meaning of something like 30° + 3. The only thing you can really add to angle (or perhaps temperature) is a change in angle (temp), so there is no ambiguity.

Yes, that was my reasoning, but his point is valid, so is Nigel's.

30° + 3 for example. In my view, the user is using degrees and therefore the 3 is in degrees, just saving keystrokes. In Nigel's opinion the 3 is in the current angle system, if in radians then you are adding 3 radians, not 3 degrees.

30°/3 also, in Helix view, the 3 is just a number, in my view the 3 is something unknown, perhaps a time, and then the result is perhaps a speed in degrees per second, hence no longer just an angle.

So I guess we have to find a way to break the ambiguity or live with it. Perhaps keep the first argument also should work for multiplication and division. If you are working on an angle and you divide it (or multiply) by 2, then it's still an angle. If you are working on a number and multiply by an angle, you should get numbers. That way the user controls the output format just by swapping arguments (and of course inverting or negating to get the right answer).
Now multiplication of angle * angle --> number, and also angle/angle --> number. Powers always give numbers, as well as 1/x.
I can see it being useful in geometry (or for surveyors) for example to bisect an angle in DMS format simply by dividing it by 2 (and here we need Helix's way or the first argument trick to make it work).