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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)
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Oct 5, 2017 5:04 PM



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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


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  ((ab)/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)



