David Little
Mathematics Department
Penn State University
Eberly College of Science
University Park, PA 16802
Office: 403 McAllister
Phone: (814) 865-3329
Fax: (814) 865-3735
e-mail:dlittle@psu.edu

The Length of a Polar Curve

The following applet approximates the length of the curve r=r(t) in Polar Coordinates for a ≤ t ≤ b. Simply enter the function r(t) and the values a, b (in radians) and 0 ≤ n ≤ 1,000, the number of subintervals. To draw a graph of the curve r=ƒ(t), let n=0.

The values a and b can be changed by simply typing a new value, such as "1.2345", "pi/2", "sqrt(5)+cos(3)", etc. You may also change these values by using the up/down arrow keys or dragging the corresponding point left or right. To move the center of the graph, simply drag any point to a new location. To label the x-axis in radians (i.e. multiples of pi), click on the graph and press "control-r". To switch back, simply press "control-r" again.

Here is a list of functions that can be used with this applet.

Use the above applet to approximate:

• π (perimeter of a circle of radius 1/2)