MHB Equal graphs polar and rectangular

AI Thread Summary
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 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
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