I decided to take a look at what I could do while playing around in Excel Spreadsheet for this investigation, and I found that at a certain point, Excel wasnÕt able to help me much but I will talk about this later in this blip.
I decided to see how long I could get a particular pattern to run. I wanted to take a set of four numbers and repeat a pattern of taking the absolute value of the differences between one number and the next and then see how long I could go before I get down to zero.
I set up my problem in this way. At first, I was putting in four numbers. I set up the Excel sheet to take the absolute value of A - B, B - C, C - D and D – A for the rows below my given numbers. This way, my sheet was automatically filled for me.
After playing around with little success on what ransom numbers I was choosing, I decided to try some that contained patterns. For example, I tried numbers like 2, 4, 8 and 16. I noticed that with certain numbers, this pattern would give me a few more repetitions than I had before. IÕm a little thick headed, so I tried several other numbers before I decided to try the pattern of exponents. Once I did this, things went pretty smoothly. It also helps that we explored this a little in class as a group.
I tried several different patterns of exponents, and I was finally able to end up with a string that lasted 54 rows using the pattern of squaring, cubing and fourth powers of a number, and then tried several whole numbers as well as decimals. However, at this point, I realized that with my technology I wasnÕt able to continue as easily. The downside to using Excel is that we are only able to input a string of numbers so long. After a string of 15 digits, Excel will not accept any more digits and will not work with a longer string.
So, one question is: Will the process always end up giving us a string of zeros? Well, at first I thought that the answer to this question was yes but after playing around and getting the string I ended up with, I began to think that the answer might be maybe not. Since I kept getting longer periods before getting that string of zeros by adding certain digits onto the string. I think that if we had a computer program that was capable of working with longer strings of digits that we would be able to generate longer and longer periods of rows before we ended up with a set of zeros. I just donÕt think that the average person is able to afford a program that will allow us to delve into this project any farther.