David Little  
Mathematics Department Penn State University Eberly College of Science University Park, PA 16802 
Office: 403 McAllister Phone: (814) 8653329 Fax: (814) 8653735 email:dlittle@psu.edu 



Tangent Circles and the Curvature of a Function
The following applet can be used to measure the curvature of the function f(x) and x=a. Simply enter the function f(x) and the values a, b and c. The applet automatically draws the unique circle through the points (a,f(a)), (b,f(b)) and (c,f(c)). As the values a, b and c approach each other, the radius of this circle approaches the radius of the circle tangent to f(x) at x=a. The curvature of f(x) at x=a is defined to be the reciprocal of the radius of this tangent circle. The values a, b, and c 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 xaxis in radians (i.e. multiples of pi), click on the graph and press "controlr". To switch back, simply press "controlr" again. Here is a list of functions that can be used with this applet.
© 2005 David P. Little Download this applet for offline viewing (includes source code). The above applet uses the Java Math Expression Parser (JEP) developed by Singular Systems 