Number and Sequence

Topics: Number, Parity, Line Pages: 2 (552 words) Published: October 8, 2007
Problem Statement:
A spiralateral is a sequence of line segments that form a spiral like shape. To draw one you simply choose a starting point, and draw a line the number of units that's first in your sequence. Always draw the first segment towards the top of your paper. Then make a clockwise 90 degree turn and draw a segment that is as long as the second number in your sequence. Continue to complete your sequence. Some spiralaterals end at their starting point where as others have no end, this will be further explained later in the write up. I explored the patterns created by length of the sequence used to create the spiralaterals. I also explored the difference in the pattern when the numbers were in a different order.

Initially I believed that all spiralaterals ended at their starting point, but I later found out that this wasn't true. I also believed that the order of the sequence of numbers wouldn't change the shape but it would simply have it turned a different way.

For each of my exploration questions I simply drew spiralaterals that satisfied the question. For example one of my questions was "Does the number of numerals in the sequence change the pattern?" To test this I drew a three number spiralateral, a 4 sequence spiralateral and a 5 sequence spiralateral, I found out that the number of numbers actually does affect the pattern of the spiralateral. I had no problems trying to solve this POW.

I had no assistance in doing this POW.

Results and Conclusions:
As I drew the spiralaterals I found that spiralaterals with an even number of numbers in each sequence tended not to end at the starting point. I also discovered that if they had an even number of numerals in the sequence, but they repeated a number then it would end. All spiralaterals with an odd number of numerals will end where the started and continue to cycle around. If a spiralateral repeats a number then it must end; this applies to all sequences whether they be odd...
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