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.wtf wrote: ↑Sat Aug 04, 2018 9:54 pmCame 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?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.

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?

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.

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.