Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.


Math Forum
»
Discussions
»
sci.math.*
»
sci.math
Topic:
How we get a Ellipse from a Conic, and how we get a Oval from Cylinder Sections knifes that are V and asymmetrical V shaped
Replies:
27
Last Post:
Oct 8, 2017 12:41 AM



Me
Posts:
1,356
Registered:
1/23/16


Re: How we get a Ellipse from a Conic, and how we get a Oval from Cylinder Sections knifes that are V and asymmetrical V shaped
Posted:
Oct 6, 2017 3:47 AM


On Friday, October 6, 2017 at 3:59:20 AM UTC+2, Archimedes Plutonium wrote:
> I already proved several times over that a cone is always a Oval section ...
No, you haven't.
In fact you will find a simple proof below that shows that certain conic sections are ellipses.
Some preliminaries:
Top view of the conic section and depiction of the coordinate system used in the proof:
^ x  + <= x=h .'  `. /  \ .  .    .  . \  / `.  .´ y <+ <= x=0 Cone (side view): /  \ /b  \ /+´ <= x = h / ´ \ / ´  \ / ´  \ x = 0 => ´+\ / a  \
Proof:
r(x) = a  ((ab)/h)x and d(x) = a  ((a+b)/h)x, hence
y(x)^2 = r(x)^2  d(x)^2 = ab  ab(2x/h  1)^2 = ab(1  4(x  h/2)^2/h^2.
Hence (1/ab)y(x)^2 + (4/h^2)(x  h/2)^2 = 1 ...equation of an ellipse
qed



