Imp 2 Pow 16 Spiarlaterals

Problem Statement

When there is a sequence of line segments that forms a spiral-like shape it is known as a spiralateral. This assignment is to explore these spiralaterals and come to up with some rules about them and state the conclusions.

Spiralaterals are usually drawn on pieces of graph paper. They are based on a sequence of numbers that can be of any length. To draw a spiralateral first pick a starting point anywhere on the paper. Then, going upward, you draw the first number in the sequence and put an arrow at the end of the line segment. Then turn clockwise 90Ð'Ñ" and draw the next number in the sequence in a line. Put an arrow at the end of that segment. Continue this pattern until it reaches the end of the numbers in the sequence. Instead of stopping there redraw the entire sequence again and again. Once you reach the original starting point it is considered finish. Some may never reach the starting point. If it completes itself count the number of steps or how many lines drawn it took to finish. After experimenting with different types of spiralaterals write the conclusions found and explain why the conclusion is true.

Process

I thought the best way to explore spiralaterals would be to split each sheet of examples into different categories. The denominations I have included are sequences with the length of three and four adding one each time, subtracting one each time, adding two, subtracting two, multiplying by two, dividing by two, and then a couple with just a random order. If the spiralateral concluded at the starting point I would count the number of steps it took and write it down. Once I was done with a particular example I would write down what I thought I could have concluded from the section.

Results and Conclusions

I have showed the results of my exploration on the graph papers following the write up. I came up with many conclusions about spiralaterals. I felt the best way to explain was in a chart so as not to be confusing. This chart is following this page. All of my conclusions were based on the spiralaterals I drew and they are what all of them had in common. I think that they hold general because no matter what numbers you have in your sequences the higher the number the larger the boxes you create in each graph will be. If the numbers get to spread out it seems