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Topic: Is MIT's Larry Guth, Sigurdur Helgason, Anette Hosoi as dumb as Dan
Christensen in thinking ellipse is a conic section when it really is an OVAL
(proofs at end of post)

Replies: 5   Last Post: Oct 5, 2017 5:04 PM

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Registered: 1/23/16
Re: Is MIT's Larry Guth, Sigurdur Helgason, Anette Hosoi as dumb as
Dan Christensen in thinking ellipse is a conic section when it really is an
OVAL (proofs at end of post)

Posted: Oct 3, 2017 9:56 AM
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On Tuesday, October 3, 2017 at 3:17:50 PM UTC+2, Archimedes Plutonium wrote:

> Here Franz is muddling through a mess

With *a little efford* the significance of the formulas (the calculation) can be figured out. You know, math is not just bla bla.

> not knowing what is a circle from oval

You obviously don't know the general equation for an ellipse.

Hint:

(1/ab)y^2 + (4/h^2)(x - h)^2 = 1

is the equation for an ellipse.

If a = b = r and h = 2r we get the equation of a circle:

(1/r^2)y^2 + (1/r^2)(x - 2r)^2 = 1

=> (x - 2r)^2 + y^r = r^2

Are you really too dumb to understand these simple things, Archie?

Here's the compliete proof again:

> > Cone/Cylinder (side view):
> >
> >                 / | \   (with b <= a)
> >                /b |  \
> >               /---+---´ <= x = h
> >              /    |´   \
> >             /   ´ |     \
> >            / ´    |      \
> >  x = 0 => ´-------+-------\
> >          /    a   |        \
> >
> > (cone: b < a, cylinder: b = a = r)
> >
> > r(x) = a - ((a-b)/h)x
> > d(x) = a - ((a+b)/h)x
> >
> > y(x)^2 = r(x)^2 - d(x)^2 = ab - ab(2x/h - 1)^2 = ab(1 - 4(x - h)^2/h^2
> >
> > => (1/ab)y(x)^2 + (4/h^2)(x - h)^2 = 1  ...equation of an ellipse


qed.

Just to look at some "properties" of this ellipse:

> > Some considerations:
> >
> > => y(h/2 + x')^2 = sqrt(ab - ab(2(h/2 + x')/h - 1)^2) = ab - ab(2x'/h)^2
> >
> > => y(h/2 + x') = sqrt(ab) * (sqrt(1 - (2x'/h)^2) ...symmetric relative to h/2 (hence Ec = cF)
> >
> > => y(h/2) = sqrt(ab) (= Gc = cH)




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