Posted on 11/08/2019 6:41:15 AM PST by Red Badger
There’s no oops there. Do you really think the problem I’m talking about disappears if you use radians? Do you think radians are magical and make the equations work out differently?
Any unit of measurement is intrinsically arbitrary, since we are the ones who assign them (except perhaps for quantum units). The math doesn’t change because you change the unit of measurement.
A complete revolution is 2π radians. It follows that the magnitude in radians of one complete revolution (360 degrees) is the length of the entire circumference divided by the radius, or 2πr / r, or 2π. Thus 2π radians is equal to 360 degrees, meaning that one radian is equal to 180/π degrees.
It follows, via observation, that the 'Radian' relates to pi in a unique way ...
“It’s a ‘natural’ derived measurement, with no need for a physical or literal standard to represent it.”
Yes, but it’s still arbitrary. A standard being arbitrary or not doesn’t depend on whether it’s related to a physical object. We can choose to use radians or degrees (or some other standard) to measure angles, and all of them accomplish exactly the same thing. Therefore, our use of one or the other as a standard is by definition arbitrary.
“A ‘degree’ can be anything, of any size value...”
No, by definition it can’t. If you decide to make a “degree” that is 1/100 of the angular total of a circle, then it’s not a “degree” anymore, it’s something else. Either way, no matter what we would decide to subdivide the circle into in order to get a “degree”, it would also give us something that had “no need for a physical or literal standard to represent it”. You don’t need a physical circle or any material object to derive a degree, it’s a purely mathematical concept, just like a radian.
“The trigonometry would be the same, jut with a different set of standards.”
Yes, exactly correct. So to get back to the point, since the math is exactly the same no matter what standard of measurement you use, what exactly is the relevance of you suggesting that I use radians? The problem remains exactly the same.
Radians are now the ‘SI’ unit of angular measurement.
In the future, we will all be using Radians along with the Metric System of measurements.
The term ‘degree’ will be relegated to temperature measurements only............
“As the ratio of two lengths, the radian is a “pure number” that needs no unit symbol.”
The degree is also similarly mathematically derived. Whether we assign it a unit symbol or not is really purely a subjective decision by humans.
“It follows, via observation, that the ‘Radian’ relates to pi in a unique way ...”
Well, really, it follows that the ratio of a circle’s radius to its circumference is a unique and defining characteristic of a circle. Pi is what is unique, radians are just a unit that we invented to measure angles in relation to that ratio, rather than any other mathematical relationship we might have chosen.
Ah, so it’s just pointless posturing and your suggestion has no real relevance to the problem. Thanks for clearing that up.
Our children and grandchildren will be taught in radians, degrees will be archaic in 50 years............
Last time I formally studied Math, it was established that there's nothing inconsistent with this theory, or contradictory to what we know.
The nice thing (or horrible?) about this is it's possible other universes aren't as far away as we assume.
We have pics of galaxies merging, and their aftermath.
Universes would be a ‘problem’...................
re: “The degree is also similarly mathematically derived.”
Nop. Artificial, arbitrary selection of value.
You’re just not getting it. Maybe some day, you will ...
I said this to my husband years ago.
I said, "Someday somebody's going to discover that the calculations they based on the Doppler Red Shift are all wrong, and then --- bam! --- every $^#$ thing goes back to the drawing board."
Just you wait and see.
If we see Voyager going by in a few years, then we’ll know.
That’s great!
That’s great!
The “Degree’ (angle measure)
From wiki -
The original motivation for choosing the degree as a unit of rotations and angles is unknown.
One theory states that it is related to the fact that 360 is approximately the number of days in a year.
Ancient astronomers noticed that the sun, which follows through the ecliptic path over the course of the year, seems to advance in its path by approximately one degree each day. Some ancient calendars, such as the Persian calendar, used 360 days for a year. The use of a calendar with 360 days may be related to the use of sexagesimal numbers.
Another theory is that the Babylonians subdivided the circle using the angle of an equilateral triangle as the basic unit and further subdivided the latter into 60 parts following their sexagesimal numeric system. The earliest trigonometry, used by the Babylonian astronomers and their Greek successors, was based on chords of a circle. A chord of length equal to the radius made a natural base quantity. One sixtieth of this, using their standard sexagesimal divisions, was a degree.
Aristarchus of Samos and Hipparchus seem to have been among the first Greek scientists to exploit Babylonian astronomical knowledge and techniques systematically. Timocharis, Aristarchus, Aristillus, Archimedes, and Hipparchus were the first Greeks known to divide the circle in 360 degrees of 60 arc minutes.[11] Eratosthenes used a simpler sexagesimal system dividing a circle into 60 parts.
The division of the circle into 360 parts also occurred in ancient India, as evidenced in the Rigveda
“Nop. Artificial, arbitrary selection of value.”
Lol. Anything that humans do is “artificial”. We didn’t find “radian” written on a rock floating in space, you know. “Radian” is defined by a mathematical formula created by humans, and “degree” is defined by another formula created by humans. Yes, we could arbitrarily pick a different amount to subdivide a circle into in order to come up with a different kind of “degree”, but I could also decide that we should measure our “radians” based on the ratio of a circumference to the diameter of a circle instead of the radius, and thus I would arrive at a “radian” that is twice the value of the one we currently have. So they are both artificial and arbitrary.
Stop spamming the forum unless you have something actually useful to contribute. Anyone can look up articles and we have all learned this stuff way back in high school anyway.
Get a grip - its NOT spam, and you started it. Did you learn somethning yet?
If’n you had a ‘brain’ in your head (you apparently don’t) you would know that calculus and the sciences use the natural radian unit ALMOST exclusively in formulas and calculations ... used to drive me crazy -
what is 60 Hz in Radians? 376.991 Radians/sec.
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