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Re: Cartesian Universal Function Re: 3-5 Chapter 3 for age 14// Teaching True Mathematics

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Archimedes Plutonium <plutonium.archimedes@gmail.com> wrote:
> On Saturday, May 19, 2018 at 1:44:40 PM UTC-5, True Mathematics Learner
> wrote:

>> Dear Professor Plutonium

>> I read your posts with great interest and would like to have a better
>> understanding of your ideas. I have a few questions for you:

>> 1. You claim that ovals are conics, not ellipses. I read proofs that
>> ellipses are indeed conic sections. Where is the flaw in these
>> proofs? What makes your proof better?

>> Regards

[ .... ]

> Now for proof that the Conic section cannot be an ellipse but an oval,
> I again would apply the same proof argument by symmetry.

> Proof:: Take a cone in general, and build a circle that rotates on a
> axis. Rotate the circle just a tiny bit for it is bound to get stuck
> or impeded by the upward slanted walls of the cone. Rotate as far as
> you possibly can. Now filling in the area upwards is far smaller than
> filling in the area downwards. Hence, only 1 axis of symmetry, not 2
> axes of symmetry. Define Oval as having 1 axis of symmetry. Thus a
> oval, never an ellipse. QED

Nice try.  The fact is, if you rotate that circle a bit (or even a lot),
the pivot is no longer at the centre of the curve, but off to one side.
If you were to consider a line parallel to that pivot, but passing
through the widest part of the curve, you would find the curve
symmetrical about that line.  And that curve is an ellipse.

[ .... ]

> --Archimedes Plutonium

-- 
Alan Mackenzie (Nuremberg, Germany).

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#3-1  Chapter 3 for age 14// Teaching True Mathematics Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-15 18:50 -0700
  3-1 through 3-3 Chapter 3 for age 14// Teaching True Mathematics Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-15 21:26 -0700
    3-4 Chapter 3 for age 14// Teaching True Mathematics Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-15 21:41 -0700
      3-5 Chapter 3 for age 14// Teaching True Mathematics Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-15 22:19 -0700
        Experimenting with ellipse & oval tubes Teaching True Mathematics Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-16 01:46 -0700
          Re: Experimenting with ellipse & oval tubes Teaching True Mathematics Earle Jones <earle.jones@comcast.net> - 2018-05-16 09:20 -0700
          Looks like AP opened up a whole new field in geometry-- Cuts Re: Experimenting with ellipse & oval tubes Teaching True Mathematics Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-16 11:05 -0700
            better hypothesis Re: Looks like AP opened up a whole new field in geometry-- Cuts Re: Experimenting with ellipse & oval tubes Teaching True Mathematics Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-17 10:53 -0700
              Re: better hypothesis Re: Looks like AP opened up a whole new field in geometry-- Cuts Re: Experimenting with ellipse & oval tubes Teaching True Mathematics Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-17 11:10 -0700
                These ideas belong in my other quest to unify Conic sections with Regular Polyhedra Re: Experimenting with ellipse & oval tubes Teaching True Mathematics Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-17 16:06 -0700
                Re: Archimedes "Failure" Plutonium flunked the lifetime-generation test moroney@world.std.spaamtrap.com (Michael Moroney) - 2018-05-18 04:19 +0000
              Re: Archimedes "Failure" Plutonium flunks the lifelong Math test moroney@world.std.spaamtrap.com (Michael Moroney) - 2018-05-17 19:16 +0000
        3-5 Chapter 3 for age 14// Teaching True Mathematics Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-16 12:43 -0700
          Cartesian Universal Function Re: 3-5 Chapter 3 for age 14// Teaching True Mathematics Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-17 21:04 -0700
            Re: Archimedes "Total Failure" Plutonium flunked the lifetime-generation test moroney@world.std.spaamtrap.com (Michael Moroney) - 2018-05-18 04:26 +0000
            Re: Cartesian Universal Function Re: 3-5 Chapter 3 for age 14// Teaching True Mathematics Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-17 21:44 -0700
              Re: Archimedes "Failure" Plutonium flunked the lifetime-generation test moroney@world.std.spaamtrap.com (Michael Moroney) - 2018-05-18 04:56 +0000
              Re: Cartesian Universal Function Re: 3-5 Chapter 3 for age 14// Teaching True Mathematics Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-18 07:01 -0700
                Re: Cartesian Universal Function Re: 3-5 Chapter 3 for age 14// Teaching True Mathematics True Mathematics Learner <francois.grondin2003@gmail.com> - 2018-05-19 11:44 -0700
                Re: Cartesian Universal Function Re: 3-5 Chapter 3 for age 14// Teaching True Mathematics Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-19 13:10 -0700
                Re: Cartesian Universal Function Re: 3-5 Chapter 3 for age 14// Teaching True Mathematics Alan Mackenzie <acm@muc.de> - 2018-05-21 09:18 +0000
        3-6, 3-7 Chapter 3 for age 14// Teaching True Mathematics Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2018-05-16 22:31 -0700

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