Graphing x^2+y^2+z^2=z: Integral & Range Help

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SUMMARY

The discussion focuses on graphing the equation x² + y² + z² = z and integrating it using spherical coordinates. The user is familiar with the concept of x² + y² + z² = k, where k is a constant, but seeks clarification on how to determine the range of the radius z in this context. A hint is provided to complete the square, suggesting that the transformation (z - z/2)² = z² - z + 1/4 may be useful for integration.

PREREQUISITES
  • Understanding of spherical coordinates in three-dimensional space.
  • Knowledge of completing the square in algebra.
  • Familiarity with integration techniques in multivariable calculus.
  • Basic concepts of graphing three-dimensional equations.
NEXT STEPS
  • Study the method of integrating functions in spherical coordinates.
  • Learn about the geometric interpretation of the equation x² + y² + z² = z.
  • Explore techniques for completing the square in various algebraic contexts.
  • Research the implications of variable radius in three-dimensional graphing.
USEFUL FOR

Students and educators in mathematics, particularly those studying multivariable calculus, as well as anyone interested in graphing three-dimensional equations and integrating them using spherical coordinates.

kthouz
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can someone help me in graphing the following function: x^2+y^2+z^2=z.
i actually know about x^2+y^2+z^2=k (k=constant) but there above the radius z still changing. the qustion was to intagrate that function and i want to use the spherical coordinates then i will need to know the range of the radius.
 
Physics news on Phys.org
Why don't you complete squares?

Hint: [itex](z-z/2)^2=z^2-z+1/4[/itex]
 

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