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- How can I parametrize a paraboloid using two or one parameter?
The discussion focuses on parametrizing the paraboloid defined by the equation z = x^2 + y^2 Two methods are presented: the first uses two parameters, u and v, where x = u, y = v, and z = u^2 + v^2, allowing for any point on the surface to be represented The second method employs a single parameter, t, resulting in x = t, y = t, and z = 2t^2 Both parametrizations effectively describe points
- Paraboloid Equations: Coordinates Relationships - Physics Forums
The discussion revolves around finding the coordinates of a paraboloid in various orthogonal curvilinear coordinate systems, particularly in relation to spherical and cylindrical coordinates The original poster seeks to understand how to express points on a paraboloid that rotates around the x-axis, drawing parallels to how spheres are represented in spherical coordinates Exploratory
- Parametric Paraboloid In Polar Coordinates • Physics Forums
The discussion revolves around finding a parametric representation of a paraboloid defined by the equation z = x² + y², specifically within the bounds of z = 0 to z = 1 The original poster explores the use of polar coordinates to express this paraboloid parametrically The original poster attempts to define a parametric form using polar coordinates, while some participants question the
- Surface Intersection: Paraboloid Plane • Physics Forums
Hello! :D Find the surface that is created by the intersection of the paraboloid $x^2+y^2-z=0$ and the plane $z=2$ Is the intesection: $x^2+y^2=2,z=2$? Or
- Stokes Theorem paraboloid intersecting with cylinder
The discussion revolves around applying Stokes' Theorem to evaluate the integral of the curl of a vector field over a surface defined by a paraboloid intersecting with a cylinder The vector field is given as F (x,y,z) = x²z² i + y²z² j + xyz k, and the surface S is the portion of the paraboloid z = x² + y² that lies within the cylinder x² + y² = 4, oriented upwards Exploratory
- Equation of a circular paraboloid • Physics Forums
The problem involves finding the equation of a surface that is equidistant from a specific plane and a point in three-dimensional space The subject area pertains to geometry, specifically the properties of surfaces and distances in three-dimensional coordinate systems Exploratory, Mathematical reasoning, Problem interpretation Participants discuss setting the distances from a point to a
- Volume under a paraboloid and above a disk • Physics Forums
The discussion revolves around finding the volume of a solid under a paraboloid defined by the equation z=x²+y² and above a disk described by the inequality x²+y²≤9, utilizing polar coordinates for the calculations Exploratory, Mathematical reasoning, Assumption checking The original poster attempts to determine the intersection point of the paraboloid and the cylinder, expressing
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