pka hates degree measure

pka

pka

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I understand functions that are defined on numbers. But what are degrees? If you say that they are numbers, then tell me what numbers?
 
A measure is a real number. In axiomatic geometry see that \(m(\angle ABC)\) is such that \(0\le m(\angle ABC)\le \pi\) .
Where are there degrees in that axiom? I just do not see it in any up-to-date textbook on geometry. OH! that may be my mistake: You are not up-to-date?
 
The point is: the use of degrees is obsolete.
 
Radians are the best. Some how people prefer degrees. Even the French have their own degrees system whish is also pretty horrible.
 
yoscar04 said:
Radians are the best. Some how people prefer degrees. Even the French have their own degrees system whish is also pretty horrible.
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I have NOT seen a protractor with π/2 angle or π/3 angles. You devise that protractor and everybody MIGHT consider radian as a measurable unit.
 
Subhotosh Khan said:
I have NOT seen a protractor with π/2 angle or π/3 angles. You devise that protractor and everybody MIGHT consider radian as a measurable unit.
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I bet that is one of the reasons why people prefer degrees. Regarding the comment Radian are best, I had very specific people in mind (physicists, mathematicians and maybe some engineers, the last one I am not completely sure). No way people can compute let's say trigonometric functions using degrees, as far as I know.
 
pka said:
If you say that they are numbers, then tell me what numbers?
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Don't blame the [MATH]^\circ[/MATH] symbol for your woes: your error is simply that you write radians as plain numbers instead of degrees.
[MATH]sin(90) = 1[/MATH] makes perfect sense, and [MATH]sin\left(\frac{pi^\triangle}{2}\right) = 1[/MATH] sounds good as well.
 
Subhotosh Khan said:
I have NOT seen a protractor with π/2 angle or π/3 angles. You devise that protractor and everybody MIGHT consider radian as a measurable unit.
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By the way, besides elementary school students, high school students, architects and civil engineers, who else is into protractor. I think last time I used one of those was 45 years ago.
 
mmm4444bot said:
A sampling of careers that use protractors. (I would add graphic designers, dressmakers, and hobbyists to that list.)

?
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Along similar lines, anyone who uses a compass (e.g. for navigation) or a GPS (if you want to be up-to-date), or otherwise uses latitude and longitude, uses degrees. Degree-minute-second measurements are outmoded (though still found here and there), but decimal degrees are very common in the real world, and need to be taught. I've never seen locations or directions given in radians.
 
Dr.Peterson said:
Along similar lines, anyone who uses a compass (e.g. for navigation) or a GPS (if you want to be up-to-date), or otherwise uses latitude and longitude, uses degrees. Degree-minute-second measurements are outmoded (though still found here and there), but decimal degrees are very common in the real world, and need to be taught. I've never seen locations or directions given in radians.
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I never wrote it doesn't have to be taught. Everybody starts with degrees and then some stay and others move to radians. I am sure that there are a lot of people that even never heard about radians. I was talking about preferences. I love the comment of real world. By the way the argument about degrees reminds me a lot the argument about what units should be used (SI, natural system, etc). There you will find people that prefer natural units but it would be really absurd to start teaching natural units without learning first the other ones like SI, English, etc.
 
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yoscar04 said:
I never wrote it doesn't have to be taught. Everybody starts with degrees and then some stay and others move to radians. I am sure that there are a lot of people that even never heard about radians. I was talking about preferences. I love the comment of real world. By the way the argument about degrees reminds me a lot the argument about what units should be used (SI, natural system, etc). There you will find people that prefer natural units but it would be really absurd to start teaching natural units without learning first the other ones like SI, English, etc.
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Did you think I was objecting to what you said? I was just adding to the discussion.

You're not the one who says degrees are obsolete, and complains whenever anyone at any level uses them.
 
Got your point. Besides radians in terms of Pi I, myself, have no intuition what so ever in terms of radians. Degrees are very easy to picture and remember. In any event some how down the road in physics most of physicists really detest the use of degrees. Still I can't imagine a pilot thinking in radians.
 
Dr.Peterson said:
You're not the one who says degrees are obsolete, and complains whenever anyone at any level uses them.
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A voice of sanity.

Most people are not very comfortable with fractions, but can cope reasonably well with whole numbers. For most day-to-day purposes, 360 degrees provides adequate accuracy without any reference to fractions due to its prime factors being 2, 3, and 5. Of course, if you believe that the only people who are to be considered human are those who have mastered calculus, then catering to the convenience of sub-humans is nonsense.

Radians are useful wherever calculus is useful and easy to work with for anyone capable of understanding calculus. Degrees are useful for many practical purposes and easy to understand for people with even the most basic mathematical understanding. There is a place for both.
 
yoscar04 said:
Got your point. Besides radians in terms of Pi I, myself, have no intuition what so ever in terms of radians. Degrees are very easy to picture and remember. In any event some how down the road in physics most of physicists really detest the use of degrees. Still I can't imagine a pilot thinking in radians.
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That's because they forget to switch - or how to switch - the mode of their calculator (degree←→radian).
 
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