PolarCurve

New in 14.1

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PolarCurve[r,{θ,θ_min,θ_max}]

gives a polar curve with radius r as a function of angle θ.

Details

PolarCurve is also known as polar graph.
PolarCurve is typically used to describe a geometric region inherently tied to direction and length from a center point.

PolarCurve[r,{θ,θ_min,θ_max}] gives a parametric curve with -position and -position corresponding to , .
PolarCurve[r,θ] is effectively equivalent to PolarCurve[r,{θ,0,2π}].
PolarCurve is a geometric region and can be used in functions such as ArcLength, Reduce and Integrate.

Examples

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Basic Examples (1)Summary of the most common use cases

Specify a polar curve:

In[1]:=1

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https://wolfram.com/xid/01yy8qnzroe-5ynqzv

Out[1]=1

Scope (2)Survey of the scope of standard use cases

Polar curve with a radius:

In[1]:=1

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https://wolfram.com/xid/01yy8qnzroe-tzj3bq

Out[1]=1

Embedding dimension:

In[11]:=11

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https://wolfram.com/xid/01yy8qnzroe-cdg3xh

Out[11]=11

Geometric dimension:

In[12]:=12

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https://wolfram.com/xid/01yy8qnzroe-ckg7bi

Out[12]=12

Arc length:

In[1]:=1

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https://wolfram.com/xid/01yy8qnzroe-e3sluj

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/01yy8qnzroe-tgn4a

Out[2]=2

Properties & Relations (2)Properties of the function, and connections to other functions

Use PolarPlot to plot a polar curve:

In[1]:=1

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https://wolfram.com/xid/01yy8qnzroe-3rlsor

Out[1]=1

Use RegionConvert to convert a polar curve to the parametric form:

In[1]:=1

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https://wolfram.com/xid/01yy8qnzroe-r29oz4

In[2]:=2

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https://wolfram.com/xid/01yy8qnzroe-hbtjm5

Out[2]=2

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