Curvilinear Polygons

Curvilinear Polygons

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The Arc drawing tool lets you make curvilinear polygons for which you can assign fill properties and find areas.  There are some limitations, however.  Since you can't construct point on two intersecting curves (except for circles), you have to connect curves with line segments.  If you want to connect two arcs, you have to first connect them with a line and move it to the intersection like this:

intersecting trig1 

To make a curvilinear polygon of the intersecting functions here are the steps:

  • Attach two lines.  
  • Make endpoints C and D β point proportional along the curves.
  • Make endpoints A and B α point proportional along the curves.
  • Draw the two arcs - select Draw / Arc, from C to A and D to B.
  • Select the sides and arcs of the polygon in order and click Construct / Polygon.
  • Double click the α's and replace them with π/4 and replace β with 5*π/4. The lines will become the intersection points.

intersecting trig2 intersecting trig3