MHB Equal graphs polar and rectangular

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The discussion focuses on the challenges of plotting equal graphs in polar and rectangular coordinates, specifically addressing discrepancies in the number of leaves produced by the equations. It highlights the necessity of squaring the equations to eliminate odd powers of r, which can lead to issues in graph symmetry. The participants note that negative powers can yield the same sign, complicating the graphing process. The conversation emphasizes the importance of ensuring all signs are positive to achieve the correct number of leaves. The insights gained from the discussion underscore the value of collaborative problem-solving in mathematics.
karush
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I couldn't get equal graphs one plot 4 leafs the other 2
 
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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.
 

Thread 'Significant figures for inherently bound values'

I have been insisting to my statistics students that for probabilities, the rule is the number of significant figures is the number of digits past the leading zeros or leading nines. For example to give 4 significant figures for a probability: 0.000001234 and 0.99999991234 are the correct number of decimal places. That way the complementary probability can also be given to the same significant figures ( 0.999998766 and 0.00000008766 respectively). More generally if you have a value that...
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