The Spreadsheet in
Mathematics Explorations
(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.
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