Visualization in Mathematics using Geometer's Sketchpad

Jon Wilkin, Northern Virginia Community College.  www.nvcc.edu/home/jwilkin 

These models require the user have The Geometer's Sketchpad, version 4, installed on their computer. The software is available from the publisher at www.keypress.com 

Algebra and Function sketches

slope - animates the similar triangles that are used in determining the equation of a line.

perpen - shows similar triangles that can be used in proving the products of slopes of perpendicular lines is -1.

sym - uses the trace feature to illustrate symmetry with with respect to either axis or the origin.

sqrt - traces the inverse of y=sqrt(x)

exponential - graphs an exponential function and traces its inverse.

piecewise defined functions - there are three lines and portions of these lines graphed, but hidden when you open this sketch. Clicking the first button shows the first line, the second button the portion to keep, then repeat with the remaining buttons. When done, hide the lines and keep the piecewise defined function. I have my students write the equation of each line as it appears, then have them restrict the domain when I click the second button. After all three portions are displayed, we write the function rule, with domain restrictions, for the piecewise defined function.

maximize linear programming - graphs a feasible region and then moves the function to be maximized through the region.

minimize linear programming - graphs a feasible region and then moves the function to be minimized through the region.