Problem:
Using the accompanying Java applet, find and graph the third degree polynomial model which best approximates the data:

Horizontal
Distance
Release
Height
5731000
534800
495600
451450
395300
337200
253100
[Extracted from Galileo's Gravity and Motion Experiments.]


Visualization:

This exploration illustrates the least squares algorithm which obtains the third degree polynomial which best approximates the data listed above. If you already have not done so, then click here to activate the Java applet.

  1. First, we enter the data above in the area in the left hand side of the applet. Use your mouse to click and place a cursor in this area.
  2. Type in 573,1000 followed by the Enter key. (573 and 1000 are separated by a comma.)
  3. Type in 534,800 followed by the Enter key.
  4. Continue to enter the remaining five pairs of numbers.
  5. On the bottom right hand side of the Applet screen you should see the word Linear; click on the nearby arrowhead.
  6. You will then see a list of three items; click on Cubic.
  7. Press on the Compute button at the bottom left-hand side of the Applet screen. The Applet will draw the collection of data points, the graph of the cubic and give you the equation of the cubic.
Note: If you want to use this Applet for other data sets then you must have at least four pairs of data to use the cubic option, three pairs of data to use the quadratic option and two pairs of data to use the linear option.


Acknowledgment:

The code for the Java Applet is a modification of code written by Bryan Lewis at the Department of Mathematics, Kent State University and which is available on his page Simple Least Squares Data Fitting Applet.