Basic Examples (2) 

Get an Association of the relevant information for a given rose curve:

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Get the number of petals and total area as an Association:

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Get the same information as a Dataset:

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Scope (2) 

Find the plot of a rose curve with positive and negative values of a:

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Decimal forms of n are acceptable and are rationalized internally to produce exact results:

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Options (2) 

Default PolarPlot options can be used for "Plot", "PetalPlot", and "OuterCurvePlot":

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Default ParametricPlot options can be used for "TotalAreaPlot":

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Applications (2) 

Depict the different rose curves for n=1/t as t increases:

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Plot the increasing and oscillating number of self-intersections (depending on the parity of t):

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Show the change in outer curve plots, which visually approach a circle:

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Plotting the surface area, the rose curve shows the progression towards π:

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Plotting the rose curve and outer curve for n=1/50 explains further why the surface area approaches π:

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Show how a single petal flattens for increasing integer values of n:

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Plot the area of a single petal against the n value:

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The above plot is explained by the "PetalTotalAreaFormula" property:

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Possible Issues (4) 

For the default number of PlotPoints, the area plot may appear choppy:

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Adding a higher value for PlotPoints may take longer, but will produce a smoother and more accurate plot:

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For non-numerical values of a, the function is left unevaluated:

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For negative, irrational or nonnumerical values of n, the function is left unevaluated:

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When no available property is called, the function is left unevaluated:

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Neat Examples (2) 

Visualize the progression of the rose curve plot for integer-valued n:

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Plotting the first 10 rose curves for integer n on one graph:

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Plotting the first 10 rational n (with numerator 1) rose curves on one graph:

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