Solving Surface Equation Homework

  • Thread starter Thread starter athrun200
  • Start date Start date
  • Tags Tags
    Surface
Click For Summary
SUMMARY

The discussion focuses on deriving the mathematical representation of a surface equation after rotation, specifically transitioning from Cartesian to polar coordinates. The general equation for a circle is established as y² + x² = f²(x), where f(x) represents the radius. The transformation into polar coordinates is confirmed with the equations x = r*cos(Θ) and y = r*sin(Θ), leading to the identity x² + y² = r². This confirms the relationship between the radius and the surface equation.

PREREQUISITES
  • Understanding of Cartesian and polar coordinate systems
  • Familiarity with surface equations and their representations
  • Knowledge of trigonometric functions and their applications
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study the derivation of surface equations in three-dimensional geometry
  • Explore the applications of polar coordinates in various mathematical contexts
  • Learn about the properties of circles and their equations in different coordinate systems
  • Investigate the relationship between trigonometric identities and geometric shapes
USEFUL FOR

Students studying mathematics, particularly those focusing on geometry and calculus, as well as educators seeking to clarify concepts related to surface equations and coordinate transformations.

athrun200
Messages
275
Reaction score
0

Homework Statement



attachment.php?attachmentid=37177&stc=1&d=1310620954.jpg


Homework Equations





The Attempt at a Solution



It seems very obvious that after rotation, it becomes a circle, so how to write it out mathematically?

That I don't know the general equation of a surface.
Is [itex]y^2+x^2=f^2(x)[/itex] the answer?


attachment.php?attachmentid=37178&stc=1&d=1310620954.jpg
 

Attachments

  • 1.jpg
    1.jpg
    14.3 KB · Views: 457
  • 2.jpg
    2.jpg
    21.8 KB · Views: 389
Physics news on Phys.org
Yes, this is the general equation for a circle

[tex]f(x)²=x²+y²=r²[/tex]

As seen in the figure, f(x)=radius

And from polar coordinates you can get the equation:

[tex]x=r*cos(\Theta)[/tex]
[tex]y=r*sin(\Theta)[/tex]
[tex]x²+y²=r²(cos²(\Theta)+sin²(\Theta))=r²[/tex]
 

Similar threads

Stokes' Theorem for a Circle in a Plane
  • · Replies 7 ·
Replies
7
Views
3K
Find all points where surface normal is perpendicular to plane
  • · Replies 4 ·
Replies
4
Views
2K
Surface of a Cylinder inside a Sphere
  • · Replies 4 ·
Replies
4
Views
2K
Divergence Theorem Verification: Surface Integral
  • · Replies 3 ·
Replies
3
Views
2K
Lagrange multipliers understanding
  • · Replies 8 ·
Replies
8
Views
2K
Stokes' Theorem, how to apply for this surface?
  • · Replies 4 ·
Replies
4
Views
2K
Flux/Surface Integral across a Plane
  • · Replies 5 ·
Replies
5
Views
2K
Minimal surface area for a fixed volume
  • · Replies 5 ·
Replies
5
Views
2K
How to evaluate a surface integral with three points?
  • · Replies 4 ·
Replies
4
Views
2K
Understanding the argument of the surface area integral
  • · Replies 7 ·
Replies
7
Views
2K