Tuesday, June 06, 2006

growing post 1 (oops its a little late)

1. What is meant by the terms "rotation symmetry" and "reflection symmetry?" How does this relate to pentominoes?Pentominoes are shapes that could be form using 5 squares. The pictures on the left are the 12 unique pentominoes.
Rotation symmetry or rotating any shape makes an identical shape of the original shape. Using the method of rotation symmetry to a pentomino will make a different but still similar pentomino. This does not make the new pentomino unique. Because it has a similar pentomino.
Reflection symmetry or flipping any shape makes a mirror image of the original shape. Also, using this method to a pentomino makes the mirror image of the original pentomino. It doesn't make the pentomino unique because it has a very similar image ^_^ .
2. Create a pattern. You must represent this pattern both pictorially ( i.e. with picture or diagram ) and with numbers. You must show the first 4 steps of your pattern.
shape # 1

shape # 2

shape # 3

shape # 4

3. Describe in words what is occurring with your pattern and if your pattern has an ending or if its continues on indefinately.
This shape is like stairs. It started as a 3 blocks by 3 blocks figure ( shape # 1 ). You keep adding the next set of blocks at the bottom and the bottom-right corner of the shape. So if you add the next set of blocks the shape will be longer at the left side and at the bottom side, like what is happening to the next 3 shapes. This pattern continues on and on forever. It adds more and more set of blocks than anyone could imagine.
4. Create a T-chart that shows what is happening with your pattern.
To get shape 6 and shape 8 you must figure out a formula that works for every shape with or without shape 1. I can't figure out the formula so what I did is count. I'll try to figure out the formula but in the mean time I'm done my post.




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