Re: Twin Parabola Puzzle/Conjecture

OK, I looked at the Hyperbolic Paraboloid and it seems to include the
parabola's that I have eluded to.... However, my graph should be less
inclusive and therefore NOT a hyper-paraboloid! The best example of my
problem is to imagine that you are given two pieces of wire (of the
same length). Then you are instructed to bend these wires into two
identical parabolic shapes or parabolas.

Then, attach the wire's vertex's together with a rubber band to
symbolize their joining together at their vertex's. At this point we
can view one parabola as being inverted relative to the other.
Finally, let's attach the upper parabola to the ceiling overhead and
let the other hang below it (like a mirror image). At this point we
can think of the two parabolas as occupying the same
plane, but we MUST change this. So, assuming the upper parabola is on
a line that runs east-west let's turn the lower parabola so that it
runs on a north-south line. THEN, we have two parabolas that share a
'common vertex' but they are no longer occupying the same plane. Their
respective planes have a related angle of 90 degrees.
Therefore, we can think of one parabola as being on the x-y plane,
while the other is either on the y-z plane ...OR....a plane parallel
to the y-z plane.

.

Relevant Pages

  • Re: parabola - conic section
    ... > sliced by a plane parallel to a lateral side of the cone, ... Let pi be some fixed plane. ... A parabola may be defined as the locus of a point, in pi, which moves so ... Let D be the line of intersection of delta and pi. ...
    (sci.math)
  • [LogoForum] Re: Parabolic curve ... `radial array of parabolas and `hoop skirt strategies
    ... But, as you are drawing a parabola on a plane already, ... scrollx 0 scrolly 0 zoom 1 ...
    (comp.lang.logo)
  • Re: Twin Parabola Puzzle/Conjecture
    ... what is meant by inclusion? ... can view one parabola as being inverted relative to the other. ... 'common vertex' but they are no longer occupying the same plane. ... to the y-z plane. ...
    (sci.math)
  • Re: Twin Parabola Puzzle/Conjecture
    ... but sharing a common vertex? ... One parabola occupies the x-y plane, ... either the y-z plane (or a plane that is parallel to the y-z plane. ...
    (sci.math)
  • Re: Twin Parabola Puzzle/Conjecture
    ... but sharing a common vertex? ... One parabola occupies the x-y plane, ... either the y-z plane (or a plane that is parallel to the y-z plane. ... infinity< y < infinity ...
    (sci.math)