MHB Surface of Revolution: Find Equation & Identify Surface

  • Thread starter Thread starter Fernando Revilla
  • Start date Start date
  • Tags Tags
    Revolution Surface
AI Thread Summary
The equation of the surface of revolution formed by revolving the curve defined by y^2 + z^2 + 2y = 0 around the y-axis is identified as a sphere. This curve can be rewritten as (y + 1)^2 + z^2 = 1, representing a circle centered at (0, -1, 0) with a radius of 1. When this circle is revolved about the y-axis, it generates a sphere. The resulting equation for the sphere is x^2 + (y + 1)^2 + z^2 = 1. Thus, the discussion effectively identifies the surface of revolution as a sphere.
Fernando Revilla
Gold Member
MHB
Messages
631
Reaction score
0
I quote a question from Yahoo! Answers

Find the equation of the surface of revolution when y^2+z^2+2y=0 is revolved about y-axis. Identify the surface of revolution.

I have given a link to the topic there so the OP can see my response.
 
Mathematics news on Phys.org
We can express $y^2+z^2+2y=0 $ as $(y+1)^2+z^2=1$, so $\gamma\equiv y^2+z^2+2y=0,x=0$ is a circle with center $(0,-1,0)$, radius $1$, and revolving about one of its diameters. As a consquence, the corresponding surface is the sphere $E\equiv x^2+(y+1)^2+z^2=1$.
 
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Back
Top