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Topic:
6) Is Wolfgang Rautenberg, Gerhard Ringel, Peter Roquette also trying to teachspread fakemath like Franz? For Conic is Oval, never ellipse (proofs provided)
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Last Post:
Oct 6, 2017 3:10 PM



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Re: 6) Is Wolfgang Rautenberg, Gerhard Ringel, Peter Roquette also trying to teachspread fakemath like Franz? For Conic is Oval, never ellipse (proofs provided)
Posted:
Oct 5, 2017 5:10 PM


On Thursday, October 5, 2017 at 9:38:21 AM UTC+2, Archimedes Plutonium want to see proofs...
...that certain cone sections as well as certain cylinder sections are ellipses.
It turns out that a cylinder can be considered as a special case of a cone in this context. Actually, there's a simple proof which works for both cases, cone and cylinder.
Some preliminaries:
Top view of the cone section and depiction of the coordinate system used in the proof below:
^ x  + <= x=h .'  `. /  \ .  .    .  . \  / `.  .´ y <+ <= x=0 Cone/Cylinder (side view): /  \ /b  \ /+´ <= x = h / ´ \ / ´  \ / ´  \ x = 0 => ´+\ / a  \
2 cases: 1.) cone: b < a, 2.) cylinder: b = a = r.
Proof:
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)^2/h^2
=> (1/ab)y(x)^2 + (4/h^2)(x  h/2)^2 = 1 ...equation of an ellipse
qed



