Thursday, May 11, 2006

James's Growing Post

Due Monday, May 15th...my birthday. I thought I should do it early so I don't get any unexpected birthday surprises, such as realizing I forgot to do it...Oops.

1. What is meant by the terms "rotation symmetry" and "reflection symmetry?" How does this relate to pentominoes? Explain these terms so that anyone who reads your post understands what you mean.

I don't know how to do this without sounding exactly like Rainer...But then again, I can't deny that he's exactly right. There are in total 12 unique pentominoes, and pentominoes are made up of 5 squares. Rotation symmetry means something to this effect: if you are arranging the blocks and you think you've found a new pentominoe, but then you check and find out that if you rotate it, it's another pentominoe that already exists, surprise! You've found rotation symmetry. It means that if you can rotate a pentominoe to turn it into one of the already existing 12 pentominoes, then the pentominoe is not unique.


Reflection symmetry is pretty close to being the same thing. Except this time, instead of rotating it, you can flip it over to turn into another pentominoe, then it isn't a unique shape.


2. Create a pattern. You must represent this pattern pictorially (i.e. With a picture or diagram) and with numbers. You must show the first 4 steps of your pattern.

My pattern is using an X pentominoe.
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 it continues indefinitely. Make sure that your explanation is clear enough that the person reading your description could understand your pattern without seeing your diagram.

I chose an X-shape pentominoe for my pattern. It looks like a cross. It starts off with a centre block, and 4 spokes leading out from it, 2 horizontal, and 2 vertical. Each spoke has one block on it. For each step of my pattern, I add one more block to each spoke of the X. I don't think my pattern needs to have an ending unless you want it to. You could probably keep adding blocks onto it until you died. It could continue on indefinitely as long as you wanted it to.

#4. Create a T-chart that shows what is happening with your Pattern. You must show the first 4 steps of your pattern with the T-chart.










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4 Comments:

At 3:43 PM, Blogger -rain- said...

good job expaining.....

 
At 7:15 PM, Blogger anonymousfroggit said...

thanks Rainer!

 
At 8:40 PM, Blogger Mr. Reece said...

good job with your explanation of your pattern. My only question is does the pentominoe really become a different pentominoe if we flip or rotate it, or does it stay the same and we are just looking at it from a different angle.

Mr. R

 
At 12:37 PM, Blogger Mr. Reece said...

Great job with the post James.

Your mark is 19/20

 

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