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

What is the basis for reason? And mathematics?

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Eodnhoj7
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### Re: The Foundation of the "degree" as relation of Geometric Form

wtf wrote:
Sat Aug 04, 2018 9:54 pm
Eodnhoj7 wrote:
Sat Aug 04, 2018 6:07 pm

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?

No, but rather it is inherently connected. While the radian may be the common measure, it is so because of the degree being the measurement system which provided its foundations. All systems of measurement, both good and bad, exists because of and through prior systems of of measurements, with the current system being the foundation for further measurement systems.

Can the radian exist without the degree considering a radian (or fraction/multiple of a radian) has a specific number of degrees?

Eodnhoj7 wrote:
Sat Aug 04, 2018 6:07 pm
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.

Yes that is what I am arguing in one respect, but because it is the relation of geometric shapes it has a constant element to it. A parts exist as both composed of and composing further parts, which applies to mathematics and geometry as well.

While the degree of the interior angles of a square may be 90 degrees because 90 squares fit in the circle....if a 100 squares where used then the nature of the interior degree within the square would be 100. What does not change is that the degree is the relation of a geometric object as a part of the circle to the circle itself as a universal geometric figure. This nature of the circle as a universal consisting of 360 degrees being defined by the relations which compose it;hence the circle is defined through the parts and the parts are defined through the circle.

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.
Actually the degree is completely natural as it merely shows a relation of parts. A 100 degrees through 100 squares or 90 degrees through 90 squares still observes that the circle is equivalent in degrees to the parts which compose it, with the parts which compose it equivalent to parts of the circle itself.

The radian....as a line extending from the center of the circle, then projecting upwards and being "bent" to fit the circle, still necessitates the 2 point of the circumference and the point in the center of the circle forming three points. The bending of a straight line to fit a circle, exists if and only if their is a straight line to begin with.

wtf
Posts: 636
Joined: Tue Sep 08, 2015 11:36 pm

### Re: The Foundation of the "degree" as relation of Geometric Form

Eodnhoj7 wrote:
Mon Aug 06, 2018 4:43 pm
No, but rather it is inherently connected. While the radian may be the common measure, it is so because of the degree being the measurement system which provided its foundations.
That's completely wrong, as I explained in my previous reply to you. If there were 359 or 478 or 3434 degrees in a circle, it would not change the radian at all. An angle of one radian is the angle that subtends an arc on a circle whose length equals the radius of the circle. That's completely independent of any definition of a degree.

As I already noted, alien mathematicians would not know what we call a degree. But they would all have discovered the idea of a radian, which is a natural angle measure inherent in the idea of a circle.

But this is the SECOND TIME I explained the exact same thing to you.

Is this the bad trigonometry forum? I think I'll register badtrig.com and redirect it to this site. I checked, the domain name is available. Tempting.

Impenitent
Posts: 1981
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### Re: The Foundation of the "degree" as relation of Geometric Form

wtf wrote:
Mon Aug 06, 2018 9:10 pm
Eodnhoj7 wrote:
Mon Aug 06, 2018 4:43 pm
No, but rather it is inherently connected. While the radian may be the common measure, it is so because of the degree being the measurement system which provided its foundations.
That's completely wrong, as I explained in my previous reply to you. If there were 359 or 478 or 3434 degrees in a circle, it would not change the radian at all. An angle of one radian is the angle that subtends an arc on a circle whose length equals the radius of the circle. That's completely independent of any definition of a degree.

As I already noted, alien mathematicians would not know what we call a degree. But they would all have discovered the idea of a radian, which is a natural angle measure inherent in the idea of a circle.

But this is the SECOND TIME I explained the exact same thing to you.

Is this the bad trigonometry forum? I think I'll register badtrig.com and redirect it to this site. I checked, the domain name is available. Tempting.
bad trigonometry forum? more like trigonometry for squares...

-Imp

Eodnhoj7
Posts: 2446
Joined: Mon Mar 13, 2017 3:18 am

### Re: The Foundation of the "degree" as relation of Geometric Form

wtf wrote:
Mon Aug 06, 2018 9:10 pm
Eodnhoj7 wrote:
Mon Aug 06, 2018 4:43 pm
No, but rather it is inherently connected. While the radian may be the common measure, it is so because of the degree being the measurement system which provided its foundations.
That's completely wrong, as I explained in my previous reply to you. If there were 359 or 478 or 3434 degrees in a circle, it would not change the radian at all. An angle of one radian is the angle that subtends an arc on a circle whose length equals the radius of the circle. That's completely independent of any definition of a degree.

As I already noted, alien mathematicians would not know what we call a degree. But they would all have discovered the idea of a radian, which is a natural angle measure inherent in the idea of a circle.

But this is the SECOND TIME I explained the exact same thing to you.

Is this the bad trigonometry forum? I think I'll register badtrig.com and redirect it to this site. I checked, the domain name is available. Tempting.

I am not talking about trigonometry, I am talking about the radian which is a foundation for trig but is not trig itself.

The radian is always a specific number of degrees regardless of whether the circle is 360 degrees or 3600 degrees.

Degrees are constant in the respect they are composed of the geometric relations composing the circle (as argued above).

The radian is constant in the respect the line extends from the center of the circle to the edge, is directed upward and curved towards the edge of the circle...the angle is constant because the line exists relative to another line.

The degree is founded in the relation geometric shapes with the circle (whether this was intended or not, but it is a constant) and the radian is founded in the relation of line with the circle....the foundation of measurement is inherently premised in a form of relativism.

wtf
Posts: 636
Joined: Tue Sep 08, 2015 11:36 pm

### Re: The Foundation of the "degree" as relation of Geometric Form

Eodnhoj7 wrote:
Tue Aug 07, 2018 4:57 pm

I am not talking about trigonometry

Don't know much about geography,
Don't know much trigonometry
Don't know much about algebra,
Don't know what a slide rule is for
But I do know that one and one is two,
And if this one could be with you
What a wonderful world this would be

https://www.youtube.com/watch?v=R4GLAKEjU4w

(annoying 15 second ad, but the song's worth it)

Eodnhoj7
Posts: 2446
Joined: Mon Mar 13, 2017 3:18 am

### Re: The Foundation of the "degree" as relation of Geometric Form

wtf wrote:
Tue Aug 07, 2018 7:42 pm
Eodnhoj7 wrote:
Tue Aug 07, 2018 4:57 pm

I am not talking about trigonometry

Don't know much about geography,
Don't know much trigonometry
Don't know much about algebra,
Don't know what a slide rule is for
But I do know that one and one is two,
And if this one could be with you
What a wonderful world this would be

https://www.youtube.com/watch?v=R4GLAKEjU4w

(annoying 15 second ad, but the song's worth it)
I win the debate.

wtf
Posts: 636
Joined: Tue Sep 08, 2015 11:36 pm

### Re: The Foundation of the "degree" as relation of Geometric Form

Eodnhoj7 wrote:
Tue Aug 07, 2018 7:43 pm

I win the debate.
Yes you're a master debater.

-1-
Posts: 1912
Joined: Thu Sep 07, 2017 1:08 am

### Re: The Foundation of the "degree" as relation of Geometric Form

wtf wrote:
Mon Aug 06, 2018 4:00 am
-1- wrote:
Mon Aug 06, 2018 3:38 am
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?
-1- wrote:
Mon Aug 06, 2018 3:38 am
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.
-1- wrote:
Mon Aug 06, 2018 3:38 am
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.
-1- wrote:
Mon Aug 06, 2018 3:38 am
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.
WTF. You wrote:

"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."

No, you do some thinking. How can a LENGTH be measure of an angle? Lengths are in one dimension, and are measured in length units, such as metres, miles, parsecs, light years.

Angles, on the other hand, are a planar dimension, and are enclosed by two straight lines.

You are CONFUSING DIMENSIONS AND UNITS BY THE WAY THEY ARE DERIVED.

A radian is defined by using a length, but it is not a length.

There are two concepts I am trying to get through to you, in vain: 1. A thing can't both be a length and an angle at the same time. 1. A definition of a physical measure may include wholly different measures, but the defined measure may or may not be of the same dimensionality as the defining measure.

Both of these two concepts are a bread-and-butter of physics. How you survived to this point without mastering these two, as your insistence shows on the ignorance about the dimensionality of radian being angle and not length, is a mystery.

===========================

For your edificiation (since you sent me to research the web! The nerve!) you can find the following just as easily as I did, and please count how many of these following definitions call a radian an ANGLE and how many call it a LENGTH. (None call it length, for your ease of perception.) Please pay special attention to how a length is used to define the angle of a radian.

The radian (SI symbol rad) is the SI unit for measuring angles, and is the standard unit of angular measure used in many areas of mathematics.

The radian is a unit of measure for angles used mainly in trigonometry. It is used instead of degrees. Whereas a full circle is 360 degrees, a full circle is just over 6 radians. A full circle has 2π radians (Roughly 6.28) As seen in the figure above, a radian is defined by an arc of a circle.

The radian is a unit of angular measure defined such that an angle of one radian subtended from the center of a unit circle produces an arc with arc length 1.

The radian is the Standard International (SI) unit of plane angular measure. There are 2 pi, or approximately 6.28318, radians in a complete circle.

Eodnhoj7
Posts: 2446
Joined: Mon Mar 13, 2017 3:18 am

### Re: The Foundation of the "degree" as relation of Geometric Form

-1- wrote:
Wed Aug 08, 2018 9:49 am
wtf wrote:
Mon Aug 06, 2018 4:00 am
-1- wrote:
Mon Aug 06, 2018 3:38 am
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?
-1- wrote:
Mon Aug 06, 2018 3:38 am
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.
-1- wrote:
Mon Aug 06, 2018 3:38 am
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.
-1- wrote:
Mon Aug 06, 2018 3:38 am
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.
WTF. You wrote:

"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."

No, you do some thinking. How can a LENGTH be measure of an angle? Lengths are in one dimension, and are measured in length units, such as metres, miles, parsecs, light years.

Angles, on the other hand, are a planar dimension, and are enclosed by two straight lines.

You are CONFUSING DIMENSIONS AND UNITS BY THE WAY THEY ARE DERIVED.

A radian is defined by using a length, but it is not a length.

There are two concepts I am trying to get through to you, in vain: 1. A thing can't both be a length and an angle at the same time. 1. A definition of a physical measure may include wholly different measures, but the defined measure may or may not be of the same dimensionality as the defining measure.

Both of these two concepts are a bread-and-butter of physics. How you survived to this point without mastering these two, as your insistence shows on the ignorance about the dimensionality of radian being angle and not length, is a mystery.

===========================

For your edificiation (since you sent me to research the web! The nerve!) you can find the following just as easily as I did, and please count how many of these following definitions call a radian an ANGLE and how many call it a LENGTH. (None call it length, for your ease of perception.) Please pay special attention to how a length is used to define the angle of a radian.

The radian (SI symbol rad) is the SI unit for measuring angles, and is the standard unit of angular measure used in many areas of mathematics.

The radian is a unit of measure for angles used mainly in trigonometry. It is used instead of degrees. Whereas a full circle is 360 degrees, a full circle is just over 6 radians. A full circle has 2π radians (Roughly 6.28) As seen in the figure above, a radian is defined by an arc of a circle.

The radian is a unit of angular measure defined such that an angle of one radian subtended from the center of a unit circle produces an arc with arc length 1.

The radian is the Standard International (SI) unit of plane angular measure. There are 2 pi, or approximately 6.28318, radians in a complete circle.
Holy shit...we agree on something for once.

-1-
Posts: 1912
Joined: Thu Sep 07, 2017 1:08 am

### Re: The Foundation of the "degree" as relation of Geometric Form

Eodnhoj7 wrote:
Wed Aug 08, 2018 3:14 pm
Holy shit...we agree on something for once.
And this is the first time I am disagreeing with WTF... I don't know where he went wrong with this. He is a fine feller, or woman-feller, whom I look up to. But here s/he WT fucked up big time. I don't understand why. Much less can I understand why s/he rejects reason, facts, and fact and reason.

I guess we all have our weak moments... god only would know, if s/he existed in the first place, I went wrong a lot of times.

By-the-by... I am not sure if you and I actually agree on principle. I haven't been reading your posts for a long time now, JohnDoe. Months. Many months.

Eodnhoj7
Posts: 2446
Joined: Mon Mar 13, 2017 3:18 am

### Re: The Foundation of the "degree" as relation of Geometric Form

-1- wrote:
Wed Aug 08, 2018 3:32 pm
Eodnhoj7 wrote:
Wed Aug 08, 2018 3:14 pm
Holy shit...we agree on something for once.
And this is the first time I am disagreeing with WTF... I don't know where he went wrong with this. He is a fine feller, or woman-feller, whom I look up to. But here s/he WT fucked up big time. I don't understand why. Much less can I understand why s/he rejects reason, facts, and fact and reason.

I guess we all have our weak moments... god only would know, if s/he existed in the first place, I went wrong a lot of times.

By-the-by... I am not sure if you and I actually agree on principle. I haven't been reading your posts for a long time now, JohnDoe. Months. Many months.
Like wise...generally your writing is for third graders so I figured why bother, considering this forum is populated by 1st graders it must be very frustrating for you...What is this world coming too? Where has all the hate gone? Strange times indeed.

wtf
Posts: 636
Joined: Tue Sep 08, 2015 11:36 pm

### Re: The Foundation of the "degree" as relation of Geometric Form

-1- wrote:
Wed Aug 08, 2018 3:32 pm

And this is the first time I am disagreeing with WTF... I don't know where he went wrong with this. He is a fine feller, or woman-feller, whom I look up to. But here s/he WT fucked up big time.
You're deranged. I won't be responding to the rest of this.

ps -- Thanks for the kind words. But to deny that one radian is the length of arc equal to the radius is insanity, an unwillingness to read the standard definition available all over the web.

pps -- Here's the source of your confusion.
-1- wrote:
Wed Aug 08, 2018 9:49 am
No, you do some thinking. How can a LENGTH be measure of an angle? Lengths are in one dimension, and are measured in length units, such as metres, miles, parsecs, light years.
Please review the concept of a metric space, and how length is defined in Euclidean space. For example what is the distance on the real line between the point x = 2 and the point x = 5? It's 3. Not 3 feet, 3 meters, or 3 light years. It's 3, a real number. In math, lengths are dimensionless. In a metric space we have a function that maps pairs of elements (x,y) to the distance between them, d(x,y), which is defined to be a real number. Look at the real line or the Euclidean plane or Euclidean 3-space. There are no feet or inches or parsecs. Distances are real numbers. Once you get this your confusion will disappear.

By the way some of this confusion is repeated in the Wiki article on radians, probably written by someone who (like you) took too much physics and not enough math. Length is dimensionless so you don't have to jump through any hoops to "divide out the units." That Wiki article is crap.

Again: A length is a nonnegative real number. Period. No units, no dimensions. Just a nonnegative real number.

ppps -- A woman-feller. Is that someone who fells women? Sounds like I'd be in trouble with the PC police if I did that.

pppps -- Bonus question. What is the distance in the Euclidean plane between the origin and the point (1,1)? When you figure this out you will be enlightened.

-1-
Posts: 1912
Joined: Thu Sep 07, 2017 1:08 am

### Re: The Foundation of the "degree" as relation of Geometric Form

Yes, yes, the whole world is wrong. Wiki, my examples, my old high school teacher, and practically everyone else you can think of asking.

An old lady is driving down Interstate 95, listening to the radio. The traffic announcer says, "Drivers, be wary of one car, of a red Subaru, driving the wrong way on I95." The old lady shakes her head: "Why, why just one car? EVERYONE is driving the wrong way."

"Again: A length is a nonnegative real number. Period. No units, no dimensions. Just a nonnegative real number." Oh my goodness gracious. You should start a new non-Euclidean non-non-Euclidean geometry. Length is a number. Just for the record, I don't agree. But you are welcome to disseminate your view. So 5 is 5, whether it's 5 miles or 5 km or 5 light years. It's all the same according to you, because length is nothing but a sheer number. (I am not being sarcastic. I'm just consistent with your system of measuring things.)

I have seen people melt down on forums before because they backed the wrong horse, so to speak, and they got so emotionally entangled in their own confusion that they temporarily lost their mind. Some of them went into what appeared to be a narcissistic rage. Then at the end they said "I was saying it all along and you, -1- were wrong, wrong, wrong!!" (-1- may not have been my moniker in other instances of another person's meltdown, but I substituted it in here for sake of smoother understanding) until I showed them their own quotes. People hate going through an experience like that.

wtf
Posts: 636
Joined: Tue Sep 08, 2015 11:36 pm

### Re: The Foundation of the "degree" as relation of Geometric Form

-1- wrote:
Wed Aug 08, 2018 10:04 pm
I have seen people melt down on forums before because they backed the wrong horse, so to speak, and they got so emotionally entangled in their own confusion that they temporarily lost their mind.
Project much?

Just answer my question. What's the distance on the Euclidean plane between the origin and (1,1)?

Also read this. https://en.wikipedia.org/wiki/Metric_space

Length is a nonnegative real number. If you don't know that you need to remedy your ignorance.

Eodnhoj7
Posts: 2446
Joined: Mon Mar 13, 2017 3:18 am

### Re: The Foundation of the "degree" as relation of Geometric Form

wtf wrote:
Wed Aug 08, 2018 10:20 pm
-1- wrote:
Wed Aug 08, 2018 10:04 pm
I have seen people melt down on forums before because they backed the wrong horse, so to speak, and they got so emotionally entangled in their own confusion that they temporarily lost their mind.
Project much?

Just answer my question. What's the distance on the Euclidean plane between the origin and (1,1)?

Also read this. https://en.wikipedia.org/wiki/Metric_space

Length is a nonnegative real number. If you don't know that you need to remedy your ignorance.
It appears you are taking a similar perspective to this thread:

Lines and Numbers are Inseperable as Relativistic Unit-Particulate?

viewtopic.php?f=26&t=23610

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