Angle of Ellipse? What is the angle of an ellipse and how can it be calculated?

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Discussion Overview

The discussion revolves around the concept of calculating the angle of an ellipse and finding the center of an ellipse that is tangent to the sides of a quadrilateral. Participants explore various interpretations of the angle of an ellipse, the properties of ellipses, and the geometric relationships involved in defining ellipses within quadrilaterals.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants question what is meant by "the angle of an ellipse," suggesting it could refer to the tangent at a point or the angle of the axes.
  • There is a mention of the "True Anomaly," which is defined as the angle between lines from a focus to the periapse and to a point on the ellipse.
  • One participant asks how to find the center of an ellipse within a quadrilateral, emphasizing the need for specific characteristics of the quadrilateral.
  • Another participant notes that constructing an ellipse tangent to all four sides of a quadrilateral may not always be possible.
  • Participants discuss the need for coordinates of the quadrilateral's vertices to determine the ellipse's center, with some expressing doubt about the feasibility of finding a solution.
  • There is a clarification that "tetralateral" is synonymous with "quadrilateral," and a participant expresses curiosity about ellipse properties.
  • Participants debate the characteristics of the trapezoid and the specific points defining it, with some asserting that the previously given points do not describe a trapezoid.
  • One participant emphasizes the complexity of the problem and suggests that the inquirer may need to work through it independently.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the interpretation of the angle of an ellipse or the feasibility of finding the center of an ellipse tangent to a quadrilateral. Multiple competing views and uncertainties remain throughout the discussion.

Contextual Notes

Participants highlight the importance of specifying the characteristics of the quadrilateral and the ellipse, indicating that the lack of precise definitions may hinder progress in the discussion.

optics.tech
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Hi everyone,

As I wasn't able to find it within my calculus book, can someone master here please tell me is there any way to find the angle of ellipse?

Thank you

Huygen
 
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optics.tech said:
Hi everyone,

As I wasn't able to find it within my calculus book, can someone master here please tell me is there any way to find the angle of ellipse?

Thank you

Huygen

What does that mean to you, "the angle of an ellipse" ? Your question is too vague to answer.

If you mean the tangent at any point on the ellipse, then that's trivial.
 
What information do you have about the ellipse? Maybe you have its equation and you want to know the angle of the axis?
 
Generally, the "zero degree" point on an ellipse is taken as the periapse, which is the point on the ellipse closest to one of the two focus points. The angular position is then generally referred to as the "True Anomaly", which is the angle between two lines, the first being from the focus to the periapse; the second being from that same focus to the point on the ellipse in question.

hth
 
Forget my previous question.

Now, I would like to ask again, if possible, can someone here please tell me how to find the center of ellipse in a given quadrilateral, which the ellipse is lying inside the quadrilateral and tangent to the four sides of the quadrilateral?
 
optics.tech said:
Forget my previous question.

Now, I would like to ask again, if possible, can someone here please tell me how to find the center of ellipse in a given quadrilateral, which the ellipse is lying inside the quadrilateral and tangent to the four sides of the quadrilateral?

You have to specify exactly the characteristics of the quadrilateral. For example if the ellipse is inside a rectangle AND their axes coincide, then they have the same center.
 
You have to specify exactly the characteristics of the quadrilateral. For example if the ellipse is inside a rectangle AND their axes coincide, then they have the same center.

What about this (please see attached image)?

This ellipse looks tangent to all of the three triangle edges, but it seems the ellipse center and the triangle center is not coinciding?
 

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optics.tech said:
What about this (please see attached image)?

This ellipse looks tangent to all of the three triangle edges, but it seems the ellipse center and the triangle center is not coinciding?
He said "rectangle", not "triangle".

As to your original question, I don't have an answer, but I'll point out that it is not always possible to construct an ellipse tangent to all four sides of a quadrilateral.
 
optics.tech said:
What about this (please see attached image)?

This ellipse looks tangent to all of the three triangle edges, but it seems the ellipse center and the triangle center is not coinciding?

Fellow, you are really not doing well here. First you post a question with insufficient information for there to be an answer then you abandon it. Then you post a question about quadrilaters but don't specify ANY of their characteristics, then you respond to my quadrilateral answer with a question that is NOT even a quatrilateral, it a tri-lateral (more commonly called a triangle).

Try asking a meaningful question with enough information for there to be a meaningful answer and perhaps someone will be able to help you. I'm not going to try any further.
 
  • #10
Fellow, you are really not doing well here. First you post a question with insufficient information for there to be an answer then you abandon it. Then you post a question about quadrilaters but don't specify ANY of their characteristics, then you respond to my quadrilateral answer with a question that is NOT even a quatrilateral, it a tri-lateral (more commonly called a triangle).

Try asking a meaningful question with enough information for there to be a meaningful answer and perhaps someone will be able to help you. I'm not going to try any further.

I am sorry...

Why I replace the quadrilateral with the triangle in my previous question is, because I can not find the center of the quadrilateral by drawing compared to the regular rectangle which is relative simple to find its center by drawing.

Also, what properties of the quadrilateral or tri-lateral is required?
 
  • #11
optics.tech said:
Also, what properties of the quadrilateral or tri-lateral is required?
Well, for instance, if you could give the coordinates of all four vertices that should be enough information to uniquely determine the answer (if there is one). However, this is an unusual enough question that I doubt anyone will know the answer off the top of their heads. It also looks to me like it would take a fair amount of work to solve. So, you may be stuck with figuring it out yourself.

May I ask why you need to know this? Do you need the answer for a completely general tetralateral? If, for instance, you were really only interested in trapezoids, it would become a lot easier.
 
  • #12
Well, for instance, if you could give the coordinates of all four vertices that should be enough information to uniquely determine the answer (if there is one). However, this is an unusual enough question that I doubt anyone will know the answer off the top of their heads. It also looks to me like it would take a fair amount of work to solve. So, you may be stuck with figuring it out yourself.

May I ask why you need to know this? Do you need the answer for a completely general tetralateral? If, for instance, you were really only interested in trapezoids, it would become a lot easier.

OK, let the four cartesian point of the vertex of the quadrilateral be A(0,0), B(2,0), C(2,1), D(-1,2).

How can I find the center point of an ellipse and plot it inside above quadrilateral which tangent to the four edge of it (the quadrilateral)?
 
  • #13
optics.tech said:
OK, let the four cartesian point of the vertex of the quadrilateral be A(0,0), B(2,0), C(2,1), D(-1,2).

How can I find the center point of an ellipse and plot it inside above quadrilateral which tangent to the four edge of it (the quadrilateral)?
May I ask why you need to know this? Do you need the answer for a completely general tetralateral? If, for instance, you were really only interested in trapezoids, it would become a lot easier.
 
  • #14
May I ask why you need to know this?

I would like to know more about an ellipse property.

Do you need the answer for a completely general tetralateral?

Does tetralateral is similar with quadrilateral, more or less?

If yes, then the answer is yes.

If, for instance, you were really only interested in trapezoids, it would become a lot easier.

Very well then, trapezoid is OK.

Just use the property (cartesian point) I post on my previous answer.
 
  • #15
optics.tech said:
I would like to know more about an ellipse property.
So, just curiosity? In that case, I think you'll get more out of it if you figure it out yourself.

You do realize, as I mentioned earlier, that answering your question would be a great deal of work for someone? It seems most appropriate that the someone be you.

Does tetralateral is similar with quadrilateral, more or less?
Yes -- sorry. That's what I meant.

Very well then, trapezoid is OK.

Just use the property (cartesian point) I post on my previous answer.
The points in your previous post do not describe a trapezoid.
 
  • #16
The points in your previous post do not describe a trapezoid.

OK, let the cartesian point of the trapezoid be A(0,0), B(3,0), C(3,1), D(1,1).
 
  • #17
Good. You have a way to unambiguously define a quadrilateral, and you have chosen one. Next question I would ask: how do you define a specific ellipse?
 
  • #18
Good. You have a way to unambiguously define a quadrilateral, and you have chosen one.

OK.

Next question I would ask: how do you define a specific ellipse?

What do you ask me back as I ask it in this discussion?

I don't know.
 
  • #19
optics.tech said:
What do you ask me back as I ask it in this discussion?
I already explained why. You are asking for a whole lot of work to be done. You have given no reason for anyone to do this work, except to satisfy your curiosity. Therefore, it seems clear to me that YOU are the person who should be doing most of the work.

I don't know.
Well THINK about it, for Pete's sake. Have an idea or two!
 

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