Tuesday, May 25, 2021

A Rose By Any Other Name

The polar equation r=a cos n(theta) graphs what's called a rose.  If n is even, the graph has 2n "petals".  If n is odd, the graph has n "petals".  Here are two rose graphs and their equations, graphed at desmos.com/calculator:

click to enlarge graphs


 

What is the equation of a rose with 6 petals?

 

(I started solving this with the belief that the answer lies in an equation with an absolute value sign, but I haven't been able to make that work yet.  I stumbled on a solution today, but it's not entirely satisfying.)

5 comments:

  1. I made the absolute value equation work--don't know what I was doing incorrectly earlier.

    My unsatisfying answer had n=1.5. Graph it and see why it was unsatisfying!

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  2. Peggy U2:33 AM

    r = abs(cos theta) - but I was hoping not to see an answer here!

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  3. I mean abs(cos(3theta)). Sorry bout that!

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