Quantifying the Physical Property of Direction.

[Mordred]

Ok so far but what does the 45 degree line represent on the ct vs x graph.

 

second question

 

In terms of y vs x what is the numerical relationship along the 45 degree line.

 

Here is a hint

 

[latex] ct=\frac{v}{c}x[/latex]

Edited May 25, 2016 by Mordred

[steveupson]

y=x

[Mordred]

Bingo. We choose c to follow the 45 degree line. Which makes plotting two Lorentz formulas easier. Time dilation and length contraction.

 

As shown here.

 

http://www.google.ca/url?q=http://www.phas.ubc.ca/~mav/p200/stnotes.pdf&sa=U&ved=0ahUKEwik27S2_fPMAhVY0GMKHb9sBA8QFggiMAU&sig2=3p5OTYqu4FQWehK27ZXdDQ&usg=AFQjCNF41YE6hVXGXB4_-GgwMsnpMn2CGg

[steveupson]

It would help a lot if someone would tell me what they think the function represented by the blue line in the graph does.

 

Does anyone have an educated guess as to what the function does?

[Mordred]

Rough guess I was going to say dihedral angle but that's incorrect.

 

Without knowing the intention of the animation in the first place from Hans directly your guess is as good as mine.

 

The math is reproducable but that doesn't necessarily show the intent.

 

For one thing Hans has several animations. Which he explains yet doesn't include details on this particular one.

Edited May 25, 2016 by Mordred

[steveupson]

The function is unlike any other that has ever existed.

 

Try and figure out what it does.

[Klaynos]

!

Moderator Note

You've "done the math", so can you run us through a worked example in thread, preferably using LaTeX?

If this didn't happen I'm closing the thread.

Also moved to speculations, check out the discussion rules for this section.

[steveupson]

[math] |\pi|[/math]

 

 

I know that this doesn't look right. It has a particular meaning. I've tried to explain it many times. What I was asking in the previous post was for Mordred to tell me what he thinks I've been trying to say.

 

I would like to know what he thinks the function does.

 

That way I can correct his misconceptions about what I am trying to say and correct his misconceptions about what the function actually does.

 

It has nothing at all to do with wobbles or dihedrals.

 

I hope you can allow the tread to continue at least until someone tells me what they think I've been saying. Everyone says it's just incoherent ramblings, but that isn't the case. A dozen pages of Q&A and for what?

 

I could easily show what I mean if I could use Mathematica, or if someone who does know how to use it would produce two more graphs of two more functions. Without someone else, besides me, doing the math, I cannot explain what the math means.

 

[math] |\pi/4|[/math] Is the worked example that has been produced for this thread. Mathematically the model has a meaning. It produces a function that has been graphed.

 

What more, specifically do you require?

 

 

[ajb]

Mathematically the model has a meaning. It produces a function that has been graphed.

By 'model' you mean animation?

 

 

What more, specifically do you require?

Ideally we would like, if it is possible and we think it most likely is for this case, an explicit forumla... something like f(x) = 'something'.

 

It is probably in the mathematica code quite explicitly.

[steveupson]

You need to apply the same trig function to two axis. Y to x and z to x. Which I think you've already applied.

 

Lol this reminds me of the problem set I had learning 3d graphics back in the trash 486 days. I asked myself how do you program a 2d screen to have a third dimension.

 

The trig functions bogged down that poor PC lol. Granted I was recalculating each pixel along a line.

 

 

What trig function?

 

This is not what you think it is.

 

The graph shows the elevation angle plotted against the tangent angle.

 

There is no other data or perspective or projection that can be used.

 

It is simply the plot of how the tangent angle changes as the elevation angle is varied.

By 'model' you mean animation?

 

 

 

Ideally we would like, if it is possible and we think it most likely is for this case, an explicit forumla... something like f(x) = 'something'.

 

It is probably in the mathematica code quite explicitly.

 

The animation is is a gif of the model, yes. The model is the cdf that was used to create the gif.

 

The author of the model assured me that that isn't the case.

 

The original problem was to try and formulate (compose) the function from the various trig operations.

 

Hans Milton found a way to implement the function in Mathematica without it being necessary to compose a function.

 

I believe that Mathematica has a spline function that creates the input/output angles for the animation.

 

If, however, you open the cdf file you can move the slider manually and for every elevation angle it will give you a corresponding tangent angle. How it does this is internal to the modeling software.

 

See post #17 here:

 

http://www.thephysicsforum.com/trash-can/9252-defining-new-function-merged.html

[Mordred]

Ok ignore the blue plane and visualize the rotation without it. Now describe that objects rotation without the blue plane.

 

Then note there is two value mentioned. The value of e and the (degrees between longitude and latitude) as one equals 0 the other equals 90 degrees.

 

So which of the three planes rotating is represented by (degrees between longitude and tangent) as the plane binding point undergoes its rotation.?

[Mordred]

Ok ignore the blue plane and visualize the rotation without it. Now describe that objects rotation without the blue plane.

 

Then note there is two value mentioned. The value of e and the (degrees between longitude and latitude) as one equals 0 the other equals 90 degrees.

 

So which of the three planes rotating is represented by (degrees between longitude and tangent) as the plane binding point undergoes its rotation.?

[steveupson]

So which of the three planes rotating is represented by (degrees between longitude and tangent) as the plane binding point undergoes its rotation.?

 

The blue plane and the green plane are a pair. Their relationship to one another is established by the surface normals of those two planes.

 

The yellow plane and the beige plane are another pair. Their relationship to one another is also established by their surface normals.

 

The model returns the function of:

 

tangent angle (blue/green) is a function of the elevation angle (yellow/beige)

For one thing Hans has several animations. Which he explains yet doesn't include details on this particular one.

 

Those others show spherical trigonometry using Napier.

[Mordred]

Think of the beige and purple planes as just the original position. Ignore blue. Your simply rotating the

The yellow and green plane described by e. As e rotates the blue plane shows the angle between the longitude and the tangent plane.

 

There you can now program this animation.

[steveupson]

Ideally we would like, if it is possible and we think it most likely is for this case, an explicit forumla... something like f(x) = 'something'.

 

It is probably in the mathematica code quite explicitly.

 

We are both on the same page in this regard

 

 

 

Because it's a function.

 

Look at the animation: http://community.wolfram.com//c/portal/getImageAttachment?filename=NSTF.gif&userId=93385

 

The little numbers that are changing at the top of the image relate to the little numbers that are changing in the rectangular box.

 

The relationship is establish through a function.

 

 

 

Also, there is a function that is different, but similar to this for every direction.

 

 

Also, there is a function that will relate these other functions to one another. <---- This is what I want.

 

... I've asked innumerable times for help expressing this function in algebraic terms.

 

I cannot make any more clear than that. It confounds me to no end that you still cannot hear what I am saying, at all.

 

Clue: whatever I'm trying to say algebraically should have a f() in it somewhere!

Think of the beige and purple planes as just the original position. Ignore blue. Your simply rotating the

The yellow and green plane described by e. As e rotates the blue plane shows the angle between the longitude and the tangent plane.

 

We can't ignore blue. Blue and green are at an angle to one another. This angle is part of the function. It is the tangent angle.

 

The tangent plane is the blue plane.

[Mordred]

Have you not noticed that value e and value "angle between longitude and tangent plane are not identical?

 

In fact they are opposite when one is zero the other is 90 degrees.

[Strange]

Yes, some trig functions. But if you won't actually do the math then it's simply a lot of handwaving, imho.

 

 

That is an extraordinary level of hypocrisy.

 

I have done the math so I do know that all the opinions about how simple (and foolish) it is are incorrect.

 

Then why don't you show us. Stop blaming other people.

 

The animation shown is for a small circle have a specific dimension and orientation.

The animation has a small circle dimension of 45 degrees latitude and is tilted 45 degrees from the horizontal such that it intersects the pole.

This produces the function that you graphed.

 

We need another animation with a small circle with a dimension of 30 degrees latitude tilted 30 degrees from horizontal such that it intersects the pole.

 

Then we need a third animation with at small circle with a dimension of 60 degrees lattitude tilted 60 degrees from the horizontal such that it intersects the pole.

 

 

Thank you for explaining what you are talking about. Anyone producing the equation you are looking for would, I assume, have that angle as a parameter.

 

The math is posted. Why can't you see that. All we have is this model.

Because you haven't posted the math. Do you know what the word "math" means? The model is not the mathematics, it is a result of the mathematics.

The function is waaaaaaaaaaaaaaaaaaaaaaaaaaaay too complicated to describe any other way, at this point in time.

 

Really? I thought it was "straightforward for someone with the skills." Make your mind up.

The function is unlike any other that has ever existed.

 

 

Prove it. Show us the math.

Mathematically the model has a meaning. It produces a function that has been graphed.

 

What more, specifically do you require?

 

 

The equations used to produce the animation.

[steveupson]

Have you not noticed that value e and value "angle between longitude and tangent plane are not identical?

 

In fact they are opposite when one is zero the other is 90 degrees.

 

Yes, of course. I believe that this is one of those instances that you spoke of earlier in the thread where pi/4 is a special case with special behavior.

[Mordred]

 

We can't ignore blue. Blue and green are at an angle to one another. This angle is part of the function. It is the tangent angle.

 

The tangent plane is the blue plane.

 

You can't define a tangent plane unless you can describe the object it is tangent to.

 

Step one describe the path of e.

Step two describe the tangent plane to path e.

 

 

Any complex math problem can be broken down into simpler steps. This is what were doing but your trying to reach the end product by ignoring what's prior to derive the end product.

[steveupson]

Thank you for explaining what you are talking about. Anyone producing the equation you are looking for would, I assume, have that angle as a parameter.

 

 

Really? I thought it was "straightforward for someone with the skills." Make your mind up.

 

The equations used to produce the animation.

 

I apologize for getting frustrated. Yes, it is either complicated or simple. One or the other.

 

The model was produce from these three animations posted to youtube. Mathematica does the rest, internally.

 

 

 

https://www.youtube.com/watch?v=ho8XCHIT-Oo

 

https://www.youtube.com/watch?v=xwjIeHC3Nb0

 

https://www.youtube.com/watch?v=6OnSZki9yp0

[Mordred]

Think of the blue as tangent to the rotation of green and yellow.

 

Describe the rotation of green and yellow first. You'll need this to describe the tangent plane.

[steveupson]

You can't define a tangent plane unless you can describe the object it is tangent to.

 

Step one describe the path of e.

Step two describe the tangent plane to path e.

 

 

Any complex math problem can be broken down into simpler steps. This is what were doing but your trying to reach the end product by ignoring what's prior to derive the end product.

 

The tangent plane contains the tangent of the small circle at the intersection point and the center of the sphere (which isn't part of a sphere, by the way).

[Mordred]

So mathematically model it. Animation isn't math. An animation uses math. If you want to create the animation you need the mathematics.

Edited May 25, 2016 by Mordred

[steveupson]

So mathematically model it. Animation isn't math. An animation uses math. If you want to create the animation you need the mathematics.

 

The input and output of a function have been provided.

 

Why is that not math?

[ajb]

The input and output of a function have been provided.

 

Why is that not math?

Specifying all inputs and all output does indeed specify a map between the sets in question. It is just not usually the best way to present things in the case of infinite sets

Edited May 25, 2016 by ajb