The Foundation of the "degree" as relation of Geometric Form

[Eodnhoj7]

The foundation of the "degree" as a relation of geometric forms.

1) The circle is the universal form through which all forms exist.

x) The triangle, as three points, exists 120 times within a circle of 360 degrees with each point acting as a degree in itself. Hence as 120 times the angles which form the interior of the triangle (from the center point) form the interior of the triangle as 120 degrees.

2) The square, as four points, exists 90 times within a circle of 360 degrees with each point acting as a degree in itself. Hence as 90 times the angles which form the interior of the square exist as internal 90 degrees.

3) The pentagon, as five points, exists 72 times within a circle of 360 degrees with each point acting as a degree in itself. Hence as 72 times the angles which form the interior of the pentagon exist as internal 72 degrees.

4) The hexagon exists 60 times with an internal degree of 60.

5) The septagon exists 51.4287 times with an internal degree of the same.

6) The octagon exists 45 times with an internal degree of the same.

7) The nonagon exists 40 times with an internal degree of the same.

The Decagon exists 36 times with an internal degree of the same.

9) The 1 directional line exists 360 times as 1 degree with the 2 directional line existing 180 times as an observation of 180 degrees.

All degree, through angulature, exists as relation and is subject to the number of relations measured, hence the degree changes with the number of "x" shapes applied to the circle. Measurement itself is relativistic.

[wtf]

Isn't the degree a man-made unit of measure that could be changed to anything else without affecting mathematics in the least? In fact once you're in high school trig and above, degrees are no longer used, and radian measure is standard. If anything's natural, it's radian measure.

[Impenitent]

Isn't the degree a man-made unit of measure that could be changed to anything else without affecting mathematics in the least? In fact once you're in high school trig and above, degrees are no longer used, and radian measure is standard. If anything's natural, it's radian measure.

the weather channel is confused

-Imp

[Eodnhoj7]

Isn't the degree a man-made unit of measure that could be changed to anything else without affecting mathematics in the least? In fact once you're in high school trig and above, degrees are no longer used, and radian measure is standard. If anything's natural, it's radian measure.

Strong point, but it is an argument of cause and effect where the radian, as a concept, is an "effect" or approximation of the "degree" in the respect that it is not just founded in the degree as 57.3 degrees but requires the degree to some extent. In simpler terms, while the radian may not "require" the degree in its entirety, because it exists approximately as 57.3 degrees it is still connected to it where the degree is the causal in the respect it came prior.

The degree is effectually founded, in the above argument through the line which can further observed as both a foundation of the degree and the radian.


The radian equally provides the foundation for the degree simultaneously:

Turns Radian Degrees Gradians
0 0 0° 0g
1/24 π/12 15° 16 2/3g
1/12 π/6 30° 33 1/3g
1/10 π/5 36° 40g
1/8 π/4 45° 50g
1/2π 1 c. 57.3° c. 63.7g
1/6 π/3 60° 66 2/3g
1/5 2π/5 72° 80g
1/4 π/2 90° 100g
1/3 2π/3 120° 133 1/3g
2/5 4π/5 144° 160g
1/2 π 180° 200g
3/4 3π/2 270° 300g
1 2π 360° 400g

https://en.wikipedia.org/wiki/Radian


Degrees are still used for measuring latitude and longitude and 360 degrees is the foundation of not just time, through the clock, but measuring further realities.

[wtf]

Strong point, but it is an argument of cause and effect where the radian, as a concept, is an "effect" or approximation of the "degree" in the respect that it is not just founded in the degree as 57.3 degrees but requires the degree to some extent. In simpler terms, while the radian may not "require" the degree in its entirety, because it exists approximately as 57.3 degrees it is still connected to it where the degree is the causal in the respect it came prior.

Came prior. Ok. So the phlogiston theory of heat is more fundamental than our modern understanding of heat because it's historically prior? By that logic whatever the cavemen thought about nuclear physics is more fundamental than what the latest Nobel prizewinner thinks. That the argument you're going with? Historical precedence as the ultimate arbiter of truth?

The degree is effectually founded, in the above argument through the line which can further observed as both a foundation of the degree and the radian.

Isn't the degree entirely arbitrary? If the Babylonians had said there are 359 degrees in a circle, or 478 degrees in a circle, we'd use that, right? Nothing would change.

ps -- Wanted to mention something else. Radian measure is natural in a way degree measure isn't. Suppose the Babylonians did make the circle 359 degrees. We'd have to redo all the degree-based trig tables. But nothing else in math would change.

But even if we did this, radians wouldn't change. A radian is a natural measure of the circumference of a circle. Namely it's the length of the circle's radius around the circumference of the circle. If space aliens show up, they won't know what a degree is. But they'll know what radians are.

[-1-]

If space aliens show up, they won't know what a degree is. But they'll know what radians are.

Because the amount of intelligence Radians, from the galaxy Radias, radiate is measured in radians?

How many radians does it take to screw in a lightbulb? (! Trick question, because it is NOT a trick question. The trick is not use a tricky reply to answer this question.)

[-1-]

A radian is a natural measure of the circumference of a circle. Namely it's the length of the circle's radius around the circumference of the circle.

I thought a radian was an angle, not a length.

As such wouldn't a radian be the angle between two straight line segments that start from the centre of a circle and end on the perimeter of the circle, which perimeter is the same length as the radius or the length of either of these two line segments?

Been a long time since high school.

[wtf]

A radian is a natural measure of the circumference of a circle. Namely it's the length of the circle's radius around the circumference of the circle.

I thought a radian was an angle, not a length.

As such wouldn't a radian be the angle between two straight line segments that start from the centre of a circle and end on the perimeter of the circle, which perimeter is the same length as the radius or the length of either of these two line segments?

Been a long time since high school.

https://upload.wikimedia.org/wikipedia/ ... adians.gif

From here ... https://en.wikipedia.org/wiki/Radian

[-1-]

I thought a radian was an angle, not a length.

As such wouldn't a radian be the angle between two straight line segments that start from the centre of a circle and end on the perimeter of the circle, which perimeter is the same length as the radius or the length of either of these two line segments?

Been a long time since high school.

https://upload.wikimedia.org/wikipedia/ ... adians.gif

This visual precisely says the very same thing as I have: radian is not a measure of length, but of an angle; and the size of the angle is determined the way I described.

Just read what I wrote, please.

Then you will see that the definition of a radian uses a length, namely, the radius of the circle; but the radian is actually an angle, with the two sides starting at the centre of the circle, and the other ends being as far apart, as their intersection with the section (part of the entire perimeter of the circle) encompasses the same length of the section as the length of the radius.

Wording this is tricky. Understanding it is trickier. The visual was good, and said precisely the same thing.

------------------

Let me put it another way: radian is a measure of angle, not of length. Period. Much like degrees are a measure of angles, not of lengths, and gradients are a measure of angle, not of length.

Let me put it another way: You can say Larry is 5 metres away from Barry, and without moving either one of them, the ANGLE at which they are separated from your viewpoint changes with your position. Hence, Angles are not measured by length; although some units of angles are defined by using length and a visual description.

This entire exercise is a comment on how you first explained radians to JohnDoe. See above.

[wtf]

I thought a radian was an angle, not a length.

A radian is a *measure* of an angle, not an angle itself. One radian is the length of the radius along the circumference. Is this something you agree or disagree with? The picture makes it perfectly clear.

Let me put it another way: You can say Larry is 5 metres away from Barry, and without moving either one of them, the ANGLE at which they are separated from your viewpoint changes with your position.

WTF? That's like saying Larry's height changes depending on how far away you are from him. No. Your perception might change based on perspective, but his height stays the same. As does any given angle.

Hence, Angles are not measured by length; although some units of angles are defined by using length and a visual description.

You are simply wrong. Radian measure is the LENGTH of the arc on the unit circle subtended by an angle. It's silly to be arguing about high school trigonometry, something that can easily be looked up by anyone.

Just read what I wrote, please.

I am, and I'm cursing your high school trig teacher. It's ok. Mine was awful too, a screechy old woman who I thought was saying "Piece of oh, piece of oh," when she was actually saying "P-sub-0."

[-1-]

I thought a radian was an angle, not a length.

A radian is a *measure* of an angle, not an angle itself. One radian is the length of the radius along the circumference. Is this something you agree or disagree with? The picture makes it perfectly clear.

Let me put it another way: You can say Larry is 5 metres away from Barry, and without moving either one of them, the ANGLE at which they are separated from your viewpoint changes with your position.

WTF? That's like saying Larry's height changes depending on how far away you are from him. No. Your perception might change based on perspective, but his height stays the same. As does any given angle.

Hence, Angles are not measured by length; although some units of angles are defined by using length and a visual description.

You are simply wrong. It's silly to be arguing about high school trigonometry, something that can easily be looked up by anyone.

Why are we fucking arguing about this?

You are making now mistakes all over the place. For instance, you write:

"Radian measure is the LENGTH of the arc on the unit circle subtended by an angle."

By "AN" angle? What the fuck is that?

That fuck, my only true friend, is the angle of a radian.

Let me ask you this way: is there a tangent value of one radian? Or a sinus value of two radians? Yes or no? If yes, then the radian is a fucking angle, not a fucking length.

I really don't know where you went wrong with this, or how or when.

[wtf]

"Radian measure is the LENGTH of the arc on the unit circle subtended by an angle."

By "AN" angle? What the fuck is that?

The radian measure of an angle is the length of the arc on the unit circle subtended by that angle. Says the same thing but maybe you like it better. You couldn't figure that out?

Why are we fucking arguing about this?

Evidently because you missed that day in high school trig and now refuse to correct your learning with a little Googling.

I really don't know where you went wrong with this, or how or when.

In your post you repeatedly confuse angles with measures of angles. That's one source of your misunderstanding. There's a simple linear scaling factor to convert degree measure to radian measure, which wouldn't fit with your theory.

Regardless, I can't argue with someone who won't correct their misunderstandings with a simple Google lookup. All the best.

ps -- I'm troubled by your misplaced certainty as well as your passion, as measured by the number of f-bombs in your recent posts. I went back over your posts and wanted to comment on this:

Let me put it another way: radian is a measure of angle, not of length.

Indeed. I agree with this.

A radian is NOT a measure of length. It is the measure of an angle. It does happen to be defined as a length.

Let's say you have an angle of 1 radian. You put the vertex of the angle at the center of a circle. Then this angle subtends an arc whose length happens to be equal to the radius of the circle. That's what 1 radian means.

Let's say you start at a point on the unit circle, and run around the circle till you come back to your starting point. You have run through an angle of 2pi radians or 360 degrees. Why do we say it's 2pi radians? It's because we have run all the way around the circumference. How far did we run? If we are on the unit circle, then the circumference is 2pi. So we say that you've run through an angle of 2pi radians.

The radian measure of an angle is defined as the length around the circumference of the arc (on the unit circle) subtended by the angle.

[Arising_uk]

… Mine was awful too, a screechy old woman who I thought was saying "Piece of oh, piece of oh," when she was actually saying "P-sub-0."

Har! Har! That reminds me about when as a mature student fresh out of Poly with a Philosophy degree I blagged my way into Imperial College to do an Msc in Foundations of Advanced IT (first course I'd done where the core books were written by my lecturers!!) and this guy kept saying subaye all through the tutorial, now normally I pride myself on asking the stupid questions as I've found others wanted to ask them as well but were too scared but this time some instinct told me best not, as I was well out of my depth here amongst mathematicians, physicists and computer science grads, so after the lesson I asked them and they were aghast I'd not heard of subscript i. "I'm in trouble here I thought." as did they.

[-1-]

WTF, I hope you have the patience to go back in this argument to three posts:
1. In which you said "wtf wrote: ↑Sat Aug 04, 2018 4:54 pm
A radian is a natural measure of the circumference of a circle. Namely it's the length of the circle's radius around the circumference of the circle."

Here you unmistakably declared that a radian is a length. You did not say it is defined by a length; you said it IS a length.

Later I objected to this; now you say
"-1- wrote: ↑Sun Aug 05, 2018 2:41 pm
Let me put it another way: radian is a measure of angle, not of length.
wtf wrote: Indeed. I agree with this."

I rest my case.

My analytical geometry teacher in high school had a Ph.D. in math. Dr. Erzsebet Koranyi. I was her star pupil. For the records.

[wtf]

WTF, I hope you have the patience

At some point I'll have to give up on this. Not quite there yet. But you are deliberately not engaging with what a radian is. What do YOU think a radian is? What is 1 radian?

to go back in this argument to three posts:
1. In which you said "wtf wrote: ↑Sat Aug 04, 2018 4:54 pm
A radian is a natural measure of the circumference of a circle. Namely it's the length of the circle's radius around the circumference of the circle."

Here you unmistakably declared that a radian is a length. You did not say it is defined by a length; you said it IS a length.

Yes, a radian is a length. Yes a radian is a length. How many more times must I say that before you understand it.

Later I objected to this; now you say
"-1- wrote: ↑Sun Aug 05, 2018 2:41 pm
Let me put it another way: radian is a measure of angle, not of length.
wtf wrote: Indeed. I agree with this."

I rest my case.

It's a length that measures an angle. How many times must I say this? That's how it's defined. Go read a book, Google a web page.

My analytical geometry teacher in high school had a Ph.D. in math. Dr. Erzsebet Koranyi. I was her star pupil. For the records.

Write to her and have her straighten you out on this.