(assignment 12)

by

Robin Kirkham

The spreadsheet is a utility that is useful for data analysis for a variety of mathematics. There are many different explorations that would show useful when working with a spreadsheet such as EXCEL.

The spreadsheet is merely a tool that provides a fast and easy exploration of large amounts of data and in constructing the data through the use of an equation(s).

This tool proves to be useful in the classroom when showing quick demonstrations without all the labor required to build the tables by hand.

Let us examine a simple sequence of numbers chosen at random an entered into a spreadsheet such that each successive row is replaced by a new entry that is figure as follows:

absolute value of A- B column 1

absolute value of B- C column 2

absolute value of C- D column 3

absolute value of D- A column 4

Will the process lead to all zeros in all 4 columns ?

example 1:
 1 56 798 123 55 742 675 122 687 67 553 67 620 486 486 620 134 0 134 0 134 134 134 134 0 0 0 0 0 0 0 0

example 2:
 4565 177 789987 1978 4388 789810 44444 2587 785422 745366 77777 1801 40056 667589 75976 783621 627533 591613 707645 743565 35920 116032 35920 116032 80112 80112 80112 80112 0 0 0 0

example 3:

 54 5 6 25 49 1 19 29 48 18 10 20 30 8 10 28 22 2 18 2 20 16 16 20 4 0 4 0 4 4 4 4 0 0 0 0

In the above 2 examples, it appears that given a sequence of numbers in A,B,C, & D the series turns to zeros prior to row 10.

When the number of columns is increased the sequence continues. It seems that with additional columns the sequence can continue on beyond that of the four column.

Conclusion:

How many iterations can be run before the sequence zeros out?

No matter how I tried eight rows prior to zeroing out was all I could get.

The problem is interesting in that it would be fun to investigate many columns doing similar things to see if there could be an algorithm or at least a projection.