2005年4月20日 · To parametrize a paraboloid, we need to express the coordinates of the points on the surface in terms of two parameters, usually denoted as u and v. In this case, we can use the parameters as follows: x = u y = v z = u^2 + v^2 This parametrization allows us to represent any point on the paraboloid by plugging in different values for u and v.

2019年12月7日 · Triple integral bounded by a sphere and paraboloid. 0. How to parameterize intersection of surfaces.

2019年9月28日 · The paraboloid has height 2 and maximum radius 2. I am asked to enter the parameterisation. p(r,t)=(x(r,t),y(r,t),z(r,t)), such that 0≤r<2 and 0≤t<2π gives the paraboloid surface above. I have been playing around on some graphing packages to find the parameterisation p(r,t), and so far I have p(r,t) = [rcos(t), rsin(t), r^2].

2021年2月13日 · For a hollow paraboloid we consider the surface area of everything but the base. This results in the equation:

2015年4月24日 · (An elliptical paraboloid) Because a circle is just a special type of ellipse (using one common definition of ellipse), a circular paraboloid (defined the same as elliptical paraboloid but with the last cross section being circular) is just a special type of elliptical paraboloid. (A circular paraboloid)

2011年4月3日 · Coordinates Paraboloid Parametric Polar Polar coordinates In summary, the conversation is about finding a parametric form for the paraboloid z=x2+y2 from z=0 to z=1. The proposed solution is to use polar coordinates as parameters u and v, with the parametric equations \vec{r}(u,v)=(vcosu,vsinu,v^{2}) and u:[0..2\pi],v:[0..1].

2008年8月5日 · I just joined this forum and I desperately need the coordinates of a paraboloid in any orthogonal curvilinear coordinates. Like a sphere is easy to present in spherical coordinates and vice versa. In the same way, I will be very thankful if someone can relate any point on a paraboloid where the paraboloid rotates from the x-axis.

2020年4月12日 · We don’t need to do this, however, as the original form of the equation of this paraboloid makes it easy to find its spectrum, which can be used to distinguish among the various types of quadric surfaces: it’s $(1,1,0,-1)$, which is the spectrum that all elliptic paraboloids have.

I need to find the volume of this paraboloid, $x^2+y^2=z,z=4y,$ using triple integrals, but have trouble determining the limits of integration.

Gaussian curvature of the paraboloid. Ask Question Asked 2 years, 6 months ago. Modified 2 years, 6 months ...