Isn't a cone symmetric in only 2 dimensions?

[Capiert]

With (the cone's) round base placed on the ground

so the apex (=tip) points upward

 let  the vertical y axis, be the rotatonal axis of symmetry.

Let the x axis be on the ground, to the right from the cone,

& the z axis also be on the ground but away from the cone & me.

Let the cone's base radius R=1 (meter)

 & the cone's height h=1 m.

 

 I know both the x & z axii of the cone's contour are symmetric

 (by rotating the cone wrt the y axis).

But the cone has a taper (the radius changes) wrt the y axis (height).

Starting with the base's radius r=1 (meter)

 on the ground,

 both x & z will decrease proportionally (x^2=z^2, r^2 = x^2 + z^2)

 to zero,

 upon reaching the cone's height h=1 (meter).

But (partially) rotating the cone (to any angle <360 degrees)

 wrt either x or z axis

 will not give the same (constant=identical) contour (x,y,z) values.

So how can the cone be (mirror) symmetrical in all 3 axii

 (as Swansont implied, in my egg thread)?

A non_symmetry must exist (e.g. the taper, slope=x/y), doesn't it?

The base radius is wider than the apex's (pointed tip).

(That's like (horizontally) cutting (or mirroring) a flower at the stem:

 the blossom does NOT resemble the roots, at all.)

 

 

Edited December 9, 2017 by Capiert

[Strange]

3 hours ago, Capiert said:

So how can the cone be (mirror) symmetrical in all 3 axii

It isn't. It has rotational symmetry about the y axis (which requires three degrees not two, to also answer the question in the title).

[Capiert]

2 hours ago, Strange said:

It isn't (mirror symmetrical in all 3 axii). It has rotational symmetry about the y axis (which requires three degrees

Degrees?

2 hours ago, Strange said:

not two, to also answer the question in the title).

 

[Strange]

7 minutes ago, Capiert said:

Degrees?

 

Sorry, dimensions (I’m going to blame my phone)

[swansont]

7 hours ago, Capiert said:

 So how can the cone be (mirror) symmetrical in all 3 axii

 (as Swansont implied, in my egg thread)?

I said no such thing. You claimed a lack of symmetry in orbits, which you claimed were not ellipses and instead egg-shaped, and that you derived these from a cone. I said that cones had symmetry. I did not say that were symmetric in all dimensions. 

[Capiert]

7 hours ago, swansont said:

I said no such thing. You claimed a lack of symmetry in orbits, which you claimed were not ellipses and instead egg-shaped, and that you derived these from a cone. I said that cones had symmetry. I did not say that were symmetric in all dimensions. 

   On 16 April 2017 at 4:09 PM, Capiert said: 

I derived it (the egg shape) from a cone cut.

!

Moderator Note

Then you did it wrong. A cone is symmetrical, and you are "deriving" an asymmetry that doesn't exist.

A cone is symmetrical, & I'm deriving an asymmetry that does not exist (from a cone)

 sure sounds (to me) like the cone has no asymmetry.

?

Edited December 9, 2017 by Capiert

[swansont]

6 minutes ago, Capiert said:

   On 16 April 2017 at 4:09 PM, Capiert said: 

I derived it (the egg shape) from a cone cut.

!

Moderator Note

Then you did it wrong. A cone is symmetrical, and you are "deriving" an asymmetry that doesn't exist.

A cone is symmetrical, & I'm deriving an asymmetry that does not exist (from a cone)

 sure sounds (to me) like the cone has no asymmetry.

?

Ellipses have the same symmetry as a cone - a symmetry around one axis. Which you were claiming does not exist in orbits.

[Capiert]

A cone is only partially symmetric,

 it is not generally symmetric for all cases (=axii).

(Was the glass half full; or (half) empty?)

32 minutes ago, swansont said:

Ellipses have the same symmetry as a cone - a symmetry around one axis. Which you were claiming does not exist in orbits.

Bohrmann also had the (orbit) excentric equations

 with + & - in the denominator & nummerator respectively, or visa versa.

That is the (same) asymmetry I mean(t).

 

Ellipses have 2 different axii of symmetry (not just 1)

 (axis major 2*a; & axis minor 2*b; (they are) at 90 degrees to each other);

 (but) a (2D) egg shape has only 1 axis of symmetry (the length, =longest axis).

Edited December 9, 2017 by Capiert

[swansont]

1 hour ago, Capiert said:

A cone is only partially symmetric,

And you claimed that orbits weren't symmetric. That's the context of my statement.

So kindly leave me out of this. 

[Capiert]

On 9 December 2017 at 6:37 AM, Capiert said:

A non_symmetry must exist (e.g. the taper, (inverse) slope=x/y), doesn't it?

Erratta1:

Sorry, slope=y/x [=rise/run; NOT x/y. My mistake=typo].

Errata2:

I also think it would be wise(r)

 to state the cone's given height as a capital H,

 (instead of h);

 like its base radius R.

So I can use h for the plane's intersection height

 in the axis of symmetry (=y axis)

when that plane starts from the (most) left side

 of the (cone's) base circumference (=perimeter).

 

Erratta3:

8 hours ago, swansont said:

And you claimed that orbits weren't symmetric. That's the context of my statement.

So kindly leave me out of this. 

I suppose you've meant my (Egg thread) slip

   On 16 April 2017 at 11:28 AM, Strange said: 

Can you present the evidence that the orbits are egg-shaped?

Capiert:

Hi Strange.

I can present evidence

that "the orbits are not symmetric

as stated above."

 

Instead (improved), should have read:

I can present evidence

that the orbits are not "that" symmetric

or

that the (single symmetric axis, 2D egg) orbits are not "completely" symmetric (as an ellipse with 2 symmetric axii=),

as stated above.

 

(But that (evidence) is only based on a (slanted) cone cut (math (derivation)=plane intersection)

that is NOT an ellipse.

A similar derivation (=slanted cut, plane intersectionon) on a cylinder produces an ellipse.

E.g. Why do I get such results,

 when the text books say otherwise?

Why bother using a cone (cut, at all),

 when a cylinder will do?

Thus something is wrong,

 please check.)

Edited December 10, 2017 by Capiert

[swansont]

7 hours ago, Capiert said:

I suppose you've meant my (Egg thread) slip

No, I meant don't quote me in this thread, and don't use out-of-context statements from my posts as justification for any of your nonsense.

Quote

   On 16 April 2017 at 11:28 AM, Strange said: 

Can you present the evidence that the orbits are egg-shaped?

Capiert:

Hi Strange.

I can present evidence

that "the orbits are not symmetric

as stated above."

 

Instead (improved), should have read:

I can present evidence

that the orbits are not "that" symmetric

or

that the (single symmetric axis, 2D egg) orbits are not "completely" symmetric (as an ellipse with 2 symmetric axii=),

as stated above.

 

(But that (evidence) is only based on a (slanted) cone cut (math (derivation)=plane intersection)

that is NOT an ellipse.

A similar derivation (=slanted cut, plane intersectionon) on a cylinder produces an ellipse.

E.g. Why do I get such results,

 when the text books say otherwise?

Why bother using a cone (cut, at all),

 when a cylinder will do?

Thus something is wrong,

 please check.)

!

Moderator Note

Saying that you can present evidence is not what was asked of you. The evidence was asked for.

Getting an answer that disagrees with mainstream physics is not evidence that mainstream physics is wrong. It is much more likely  evidence that you have made a mistake. But since you don't actually present any evidence, nobody can see where that mistake was made.

The egg thread was locked, and Klaynos presented a link showing how you can derive elliptical orbits from Kepler (and thus, by extension, Newton). You don't get bring it up in another thread. The question asked in the OP has been answered.