Circle.

[Aeschylus]

i seem to understand it is irrelavent and mostly already stated was incorrect in this scenario.

 

No what you don't understand is that angles in such spaces cannot be defined by arbitary circles centred on the vertex like they are in plane geomerty. A full rotation is still 2pi radians.

[Dave]

i seem to understand it is irrelavent and mostly already stated was incorrect in this scenario.

 

I'm starting to become a bit dubious about this thread as a whole; it seems to be going in a constant circular debate and I'd rather it didn't continue if some conclusion isn't drawn soon. Posts like this add nothing to the quality of the thread, which is hanging on by its teeth as it is. I also don't want spam hanging around on these forums, so if people don't have anything more to add to the debate, then please don't add it as we'll just be prolonging things.

[Sayonara]

it seems to be going in a constant circular debate

At the risk of undermining your anti-spam comments, I just wanted to say "lol".

[ydoaPs]

No what you don't understand is that angles in such spaces cannot be defined by arbitary circles centred on the vertex like they are in plane geomerty. A full rotation is still 2pi radians.

 

see, a full rotation is 2PI radians. pi is no longer applicable. i don't have a problem with a no answer, my problem is with your reasoning. why can't the angle be defined by the space it is in?

[Dave]

At the risk of undermining your anti-spam comments, I just wanted to say "lol".

 

Admittedly, that was a rather silly choice of wording.

 

You get the idea though.

[paganinio]

I don't see what the point of the poll is' date=' seeing as it's not a matter of opinion, and the discussion itself is already underway.

 

I'm not interested in whether or not you think I have a problem.[/quote']

 

HORRIBLE...

[Sayonara]

HORRIBLE...

Nonsense. I am lovely.

[ydoaPs]

I have come to the conclusion that the measure of an angle would change. The reasoning has nothing to do with the fact that pi is no longer 3.14......

 

Draw an angle with a measure of [math]{\pi}/2[/math] radians. have a line connecting two points on the sides of the angle. That line will shring due to the spinning. The radius stays the same. Since the distance between the two sides is smaller at the same distance from the center, the measure of the angle is smaller than before the spinning.

 

Is this a type of geometry, or am do I have no way of checking my posts?

[ydoaPs]

I guess my question is "Is there already a form of geometry that deals with spinning circles, or do I have to make it up as i go?"

[ydoaPs]

It is time for my crappy diagram. the arrows are to show the direction of the rotation.

 

The distance between A and B shrinks as it spins, yet r stays the same.

 

The distance between C and D shrinks as it spins, but the radius stays the same.

 

Angle [math]\theta[/math] is [math]{\pi}/2[/math]radians while still, yet is smaller when spinning.

[ydoaPs]

[math]\pi=\frac{C\sqrt{1-\frac{V^2}{c^2}}}{d}[/math]

 

C is curcumference, c is speed of light. d is diameter

 

 

here is one for angles:

 

[math]\theta=\frac{\theta'}{\pi}*\frac{C\sqrt{1-\frac{V^2}{c^2}}}{d}[/math]

 

pi in the second equation is the euclidean pi

 

to get the [math]\theta[/math] into degrees, multiply [math]\theta[/math] by [math]\frac{180}{\frac{C\sqrt{1-\frac{V^2}{c^2}}}{d}}[/math]

[Aeschylus]

Differential geometry deals with this.

 

What happens when you change the size of the circle that you use to measure the angle? The answer is according to the way you've defined the angle, the size of the angle changes! So you can't define an angle from any old circle as on such a surface the ratio depends on the size of the circle (and possibly where the circle is). However as the radius of the circle tends to zero the ratio always tends to pi, so you can deine the angle from the point where the two lines intersect.

[NavajoEverclear]

Damn it - I spent a good few minutes hunting out [thread=381]this ancient thread[/thread'], but its relevance is diminished somewhat by the question not ever being answered.

 

I remember that thread! My reply on it was a more than a little retarded though, i think i'll edit it.

 

This thread looks like lots of fun too.

Why the hell am i still here?

[Dave]

Who knows?

 

Anyway, I think I've just about had enough of this thread. We've pretty much exhausted the topic, so I'm going to close it unless anyone has major objections.

[Dave]

Re-opened again. Please don't regurgitate all the old stuff from the thread or I'll close it permenantly - it's already 5 pages long and 90% of it is repeated.

[ydoaPs]

the size of the circle has no influence on the measurement of the angle.

[AtomicMX]

neither the speed, thought a circle is an ideal abstract ent.

[ydoaPs]

how doesn't it affect it? i have an equation to back me up, do you?

[123rock]

Differential geometry deals with this.

 

What happens when you change the size of the circle that you use to measure the angle? The answer is according to the way you've defined the angle' date=' the size of the angle changes! So you can't define an angle from any old circle as on such a surface the ratio depends on the size of the circle (and possibly where the circle is). However as the radius of the circle tends to zero the ratio always tends to pi, so you can deine the angle from the point where the two lines intersect.[/quote']

 

All circles are similar, no angle change and there would be an angular speed change or w, since the circumference will get either bigger or smaller (given).

If the circumference gets smaller w increases if the linear speed remains the same, since a bigger percentage and thus a greater angle will be covered per t, the time. Vice versa if C increases.

 

The linear speed of a circle is just arclength/time. The fact that C becomes bigger doesn't have an effect. I see what your confusion might be.

The linear speed doesn't change because the arclength is the length m of the arc/second or t time, not an actual arc percentage of C, which would make a cirlce have a linear speed of only one speed which is ridiculous.

 

So linear speed is not proportional to the circumference, angular speed increases with decrease in C, and decreases with increases in C.

[Aeschylus]

All circles are similar' date=' no angle change and there would be an angular speed change or w, since the circumference will get either bigger or smaller (given).

If the circumference gets smaller w increases if the linear speed remains the same, since a bigger percentage and thus a greater angle will be covered per t, the time. Vice versa if C increases.

 

The linear speed of a circle is just arclength/time. The fact that C becomes bigger doesn't have an effect. I see what your confusion might be.

The linear speed doesn't change because the arclength is the length m of the arc/second or t time, not an actual arc percentage of C, which would make a cirlce have a linear speed of only one speed which is ridiculous.

 

So linear speed is not proportional to the circumference, angular speed increases with decrease in C, and decreases with increases in C.[/quote']

 

I did not say the angle changes, what I said is that the way that youdagonapogos has decided to define the angle the angle changes, because he has defined it in a way that is dependent on the ratio of the diamter and the circumefrence of an arbitary circle which is not a constant in non-Euclidian spaces

 

The actual defintion of an angle theta between two vectors in a vector space where the scalar product (<x|y>) has been defined is:

 

[math]\cos{\theta} = \frac{\langle x|y\rangle}{\sqrt{\langle x|x\rangle}\sqrt{\langle y|y\rangle}}[/math]