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geft
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The equation is z = y^3. I know how to do normal planes and spheres, but I don't know what to set for r(u,v) when it comes to paraboloid cylinders.
geft said:The equation is z = y^3. I know how to do normal planes and spheres, but I don't know what to set for r(u,v) when it comes to paraboloid cylinders.
geft said:x = u
y = v
z = v^3
r(u, v) = [u, v, v^3]?
Is there a formula for the r(u, v)?
A paraboloid cylinder is a three-dimensional shape that resembles a cylinder with a parabolic cross section. It is formed by taking a parabola and rotating it around its axis, creating a curved surface that extends infinitely in both directions.
A paraboloid cylinder can be represented parametrically using two parameters, u and v, which represent the angle of rotation and the distance from the axis, respectively. The parametric equations for a paraboloid cylinder are x = v*cos(u), y = v*sin(u), and z = v^2.
The advantage of using parametric representation for a paraboloid cylinder is that it allows for a more flexible and precise description of the shape, compared to using standard equations or geometric formulas. It also allows for easy manipulation of the shape and its parameters.
A paraboloid cylinder and a parabolic cylinder are both three-dimensional shapes with a parabolic cross section, but they differ in their overall shape. A paraboloid cylinder has a curved surface that extends infinitely in both directions, while a parabolic cylinder is a finite shape with flat circular faces.
Paraboloid cylinders have many practical applications, such as in the design of satellite dishes, reflector antennas, and parabolic mirrors for solar energy collection. They are also used in architecture for creating unique building designs and in engineering for creating curved surfaces in various structures.