Wolfram Function Repository
Instant-use add-on functions for the Wolfram Language
Function Repository Resource:
Compute the properties of a specified rose curve
ResourceFunction["RoseCurveProperties"][a,n] gives an association of properties related to the rose curve with polar formula r=aSin[n θ]. | |
ResourceFunction["RoseCurveProperties"][a,n,prop] gives the values of the specified properties in prop. | |
ResourceFunction["RoseCurveProperties"][a,n,prop,format] gives the values of the specified properties in prop as either an Association or a Dataset determined by format. |
"Equation" | equation of the rose curve |
"Plot" | plot of the rose curve |
"PetalPlot" | plot of a single petal |
"PetalCount" | number of petals |
"PetalTotalAreaFormula" | formula for the total area of a single petal |
"PetalTotalArea" | total area of a single petal |
"InactiveTotalAreaIntegral" | inactive double integral for the total area of the rose curve |
"InactiveTotalAreaSingleIntegral" | inactive single integral for the total area of the rose curve |
"TotalAreaFormula" | formula for the total area of a rose curve (for rational n, rewrite n as the reduced fraction p/q) |
"TotalArea" | total area of the rose curve |
"TotalAreaPlot" | plot of the rose curve where darker hues correspond to overlapped sections |
"PetalArcLength" | arc length of a single petal |
"ArcLength" | arc length of the rose curve over one full period |
"IntersectionCount" | number of times the rose curve self-intersects |
"ClosedDomain" | interval of angles where the rose curve makes a complete cycle |
All | all properties associated with the given value of n |
"PetalSurfaceAreaFormula" | formula for the surface area of a single petal |
"PetalSurfaceArea" | surface area of a single petal |
"InactiveSurfaceAreaIntegral" | inactive double integral for the surface area of the rose curve |
"InactiveSurfaceAreaSingleIntegral" | inactive single integral for the surface area of the rose curve |
"SurfaceAreaFormula" | formula for the surface area of the rose curve (n is expressed as the reduced fraction p/q) |
"SurfaceArea" | surface area of the rose curve |
"OuterCurveEquation" | piecewise function for the outline of the rose curve |
"OuterCurvePlot" | plot of the outline of the rose curve |
Get an Association of the relevant information for a given rose curve:
In[1]:= |
Out[1]= |
Get the number of petals and total area as an Association:
In[2]:= |
Out[2]= |
Get the same information as a Dataset:
In[3]:= |
Out[3]= |
Find the plot of a rose curve with positive and negative values of a:
In[4]:= |
Out[4]= |
Decimal forms of n are acceptable and are rationalized internally to produce exact results:
In[5]:= |
Out[5]= |
Default PolarPlot options can be used for "Plot", "PetalPlot" and "OuterCurvePlot":
In[6]:= |
Out[6]= |
Default ParametricPlot options can be used for "TotalAreaPlot":
In[7]:= |
Out[7]= |
Depict the different rose curves for n=1/t as t increases:
In[8]:= |
Out[8]= |
Plot the increasing and oscillating number of self-intersections (depending on the parity of t):
In[9]:= |
Out[9]= |
Show the change in outer curve plots, which visually approach a circle:
In[10]:= |
Out[10]= |
Plotting the surface area, the rose curve shows the progression toward π:
In[11]:= |
Out[11]= |
Plotting the rose curve and outer curve for n=1/50 explains further why the surface area approaches π:
In[12]:= |
Out[12]= |
Show how a single petal flattens for increasing integer values of n:
In[13]:= |
Out[13]= |
Plot the area of a single petal against the n-value:
In[14]:= |
Out[14]= |
The preceding plot is explained by the "PetalTotalAreaFormula" property:
In[15]:= |
Out[15]= |
For the default number of PlotPoints, the area plot may appear choppy:
In[16]:= |
Out[16]= |
Adding a higher value for PlotPoints may take longer, but will produce a smoother and more accurate plot:
In[17]:= |
Out[17]= |
For non-numerical values of a, the function is left unevaluated:
In[18]:= |
Out[18]= |
For negative, irrational or non-numerical values of n, the function is left unevaluated:
In[19]:= |
Out[19]= |
When no available property is called, the function is left unevaluated:
In[20]:= |
Out[20]= |
Visualize the progression of the rose curve plot for integer-valued n:
In[21]:= |
Out[21]= |
Plotting the first 10 rose curves for integer n on one graph:
In[22]:= |
Out[22]= |
Plotting the first 10 rational n (with numerator 1) rose curves on one graph:
In[23]:= |
Out[23]= |
This work is licensed under a Creative Commons Attribution 4.0 International License