Monday, May 15, 2006

Tears' Growing Post!

Question #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.

Rotation summetry is a symmetry that is about some or all rotations so it is about a figure or an object that can be rotated on its axis . Like the picture below, the 2nd shape looks different on that angle but if you rotate it in 180 degrees, it is going to look like the first shape and that's how rotation symmetry works. Two objects might look different in a different angle but if you try to rotate one object, then it will look like the other object. Here is an example of Rotation symmetry.

Reflection symmetry is a symmetry with respect to reflection so it is about a figure or object that is flipped or reflected like a mirror. Like in the shapes below, shape 1 is the original one and shape 2 is just a reflection because if you flip it vertically it will look like shape 1. That's how Reflection symmetry works forexample :Two shapes might look different in a different angle but if you try to flip one object, then it will look like the other object. Here is an example of Reflection symmetry:

A pentomino is a polyomino composed of five congruent squares, connected orthogonally (which means perpendicularly) and it the squares has to be side by side not just the corner touching another square. We also learned that you could make up 12 different pentominoes and it has to be unique which means you can't rotate or flip your original pentomino to make a new one. Here are the 12 different pentominoes:


Rotation symmetry and Reflection symmetry relate to pentominoes because anyway you rotate or reflect a pentomino, it will not turn it into a unique pentomino if it looks the same as another pentomino.

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



Question #3: Describe in words what is occuring with your pattern and if your pattern has an ending or if it continues on indefinately. Make sure that your explanation is clear enough that the person reading your description could understand your pattern without seeing your diagram.

The shape obove is shaped like a capital e. It looks like this: E , but bigger. In Shape 1, the top part of the letter E has 3 boxes shaded in. The middle part of the letter E has 2 boxes shaded in. The lower part of the E has 3 boxes shadedd in. The pattern goes like this: You shade one more box to the top part, one more to the middle part and one more to the lower part for every new shape of the letter E. Remember you shade the box next to the last box on the top part, middle part and lower part and not below it. Also remember in shape 1, the vertical line has 5 boxes shaded in but on the pattern you don't shade another box to that vertical line only to the top part , middle part and lower part of the E. On Shape 2, 3 and 4, I colored the boxes green. Those are the boxes you add to every new shape. This pattern can even continue on indefinately.

Question #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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1 Comments:

At 12:19 PM, Blogger Mr. Reece said...

Wow, this growing post will be added to the growing post hall of fame. Great work Tears!

Your mark is 21/20

 

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