Right conoid
In geometry, a right conoid is a ruled surface generated by a family of straight lines that all intersect perpendicularly to a fixed straight line, called the axis of the right conoid.
Using a Cartesian coordinate system in three-dimensional space, if we take the z-axis to be the axis of a right conoid, then the right conoid can be represented by the parametric equations:
where h(u) is some function for representing the height of the moving line.
Examples
A typical example of right conoids is given by the parametric equations
The image on the right shows how the coplanar lines generate the right conoid.
Other right conoids include:
- Helicoid:
- Whitney umbrella:
- Wallis's conical edge:
- Plücker's conoid:
- hyperbolic paraboloid: (with x-axis and y-axis as its axes).
gollark: I don't screenshot *everything* because scrolling is at least 3 work.
gollark: I'm not sure where that would come from. Possibly people just read a lot of "people discussing it and suggesting changes" as "they dislike it".
gollark: This is indeed HIGHLY transparent.
gollark: This is documented, yes.
gollark: Maybe they just made it count all the users and never expected it to be a problem.
See also
External links
- "Conoid", Encyclopedia of Mathematics, EMS Press, 2001 [1994]
- Right Conoid from MathWorld.
- Plücker's conoid from MathWorld
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