Equal graphs polar and rectangular

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SUMMARY

The discussion centers on achieving equal graphs in polar and rectangular coordinates, specifically addressing the equation $$(x^2+y^2)^3=(10xy)^2$$. The key issue identified is the necessity of squaring the equation to avoid odd powers of $r$, which complicate the graphing process. The participants highlight that negative powers yield the same sign, necessitating all signs to be positive to generate the correct number of leaves in the graph. The use of MSB (presumably a software tool) was crucial in visualizing the problem.

PREREQUISITES
  • Understanding of polar and rectangular coordinate systems
  • Familiarity with graphing equations involving powers
  • Knowledge of the implications of odd and even powers in mathematical equations
  • Experience with graphing software, particularly MSB
NEXT STEPS
  • Research the properties of polar equations and their graphical representations
  • Learn about the implications of odd versus even powers in mathematical functions
  • Explore advanced graphing techniques using MSB software
  • Study the transformation of equations between polar and rectangular forms
USEFUL FOR

Mathematicians, educators, students studying graph theory, and anyone interested in visualizing complex equations in polar and rectangular formats.

karush
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I couldn't get equal graphs one plot 4 leafs the other 2
 
Last edited:
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You need to square again so that you don't have an odd power of $r$ (can you explain why an odd power is a problem?):

$$(x^2+y^2)^3=(10xy)^2$$
 
Not real sure on this one but negative powers return the same sign apparently we needed all signs to be positive. Not sure how this generated the 2 other needed leafs

But I would have never seen this without MSB.
 

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