Department of Mathematics Education
J. Wilson, EMAT 6680

by David Wise

Spreadsheets are an extremely useful tool in mathematical investigations, presentations, and simulations. An essential feature should be the ability to make graphs and charts. There are a great deal of spreadsheets available, such as EXCEL, WINGS, or ClarisWorks. In addition, many spreadsheets designed specifically for statistical analysis are available, such as MINITAB and FATHOM. I have used MINITAB and feel it is an outstanding piece of software. For more information, you can visit Addison Wesley Longman's website at http://hepg.awl.com, keyword: MINITAB. For more information about FATHOM, contact Key Curriculum Press.

It is important for high school students to receive exposure to commom spreadsheet applications, such as EXCEL. The ability to use spreadsheet applications has become increasingly more important for college students and employees in today's workforce.

The following investigation is carried out using EXCEL. It is a great investigation for students who are beginners with spreadsheet software. As students learn to use the capabilities of EXCEL, the value of the tool becomes very apparent. In addition, the mathematics of the investigation are not very difficult, but challenge the student with discovery.

• Place four numbers in the first row as follows:

A B C D

 3 7 21 -8

• For each successive row replace the entries by the absolute value of the difference of the entry just above and the entry just to the right in the previous row. In the fourth position, use the absolute value of the difference of the fourth and the first.

|A-B| |B-C| |C-D| |D-A|

 3 7 21 -8 4 14 29 11 10 15 18 7 5 3 11 3 2 8 8 2 6 0 6 0 6 6 6 6 0 0 0 0

In the eighth row, we get a row of all zeros.

• Will this process always lead to a zero in all four entries for a particular row?

Another trial.

 15 3848.2 -216 309.932 3833.2 4064.2 525.932 294.932 231 3538.27 231 3538.27 3307.27 3307.27 3307.27 3307.27 0 0 0 0

In the fifth row, we get a row of all zeros.

After repeated trials, it does in fact appear that the process will always lead to a zero in all four entries of a particular row.

• What is the largest number of rows before a zero row is generated?

It is not too difficult to generate up to eight rows before a zero row is generated, but is it possible to generate ten or more rows before a zero row is generated?

If you have any comments concerning this investigation that would be useful, especially for use at the high school level, please send e-mail to esiwdivad@yahoo.com.