Symmetry of a graph. SymmT(A)?

In summary: And there you have your definition of SymmT immediately prior to Example 10 in your pdf.And so, if you have a set of vectors in a space and you want to reflect them in a certain direction, you would take the union of the results.
  • #1
Matriculator
51
0
I've tried looking all over, but haven't been able to find explanations. I was wondering if anyone could provide me links to learn more about these- what's in the picture. Or if you can explain. I have already turned this work in so I'm not looking for the answers, I want explanations. I know how to reflect the figures but what do they mean by SymmT(A) sets? Thank you.
 

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  • #2
Can you sketch the graphs that result from the transformations?
##Symm_T(A)## is something special to your course?
 
  • #3
Simon Bridge said:
Can you sketch the graphs that result from the transformations?
##Symm_T(A)## is something special to your course?

Yeah. The first one will result in an upside down(in relation to the first) parabola, with the same Xs but different Ys, it will be located in the 4th quadrant.

The second one just flips over the Y-axis retaining the Ys but having different Xs. It'll be located in the 2nd quadrant.

I know how to all all of this, but my question is whether that's all I need to do in this case. Or do I need to find the ##Symm_T(A)##, based on the question asked. I'm not sure of what's that exactly. I'm trying to learn more about it but whenever I look online, nothing of the sort comes up. This is for a pre-calc class.
 
  • #4
As Simon indicated, you need to know the definition of SymmT, and it does not appear to be anything standard. It must be defined in your course notes somewhere.
 
  • #5
haruspex said:
As Simon indicated, you need to know the definition of SymmT, and it does not appear to be anything standard. It must be defined in your course notes somewhere.

Oh, sorry about that. It's from this lesson. Thank you all very much for helping. This is driving me nuts. I've been a lot behind on my college courses, but I need to know this. Except for this sheet in class and explanations which I wasn't following through well due to a lack of sleep the previous night, there's literally nothing else including the textbook, which these don't seem to be a derived from, that I can learn about this.
 

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  • #6
Matriculator said:
Oh, sorry about that. It's from this lesson. Thank you all very much for helping. This is driving me nuts. I've been a lot behind on my college courses, but I need to know this. Except for this sheet in class and explanations which I wasn't following through well due to a lack of sleep the previous night, there's literally nothing else including the textbook, which these don't seem to be a derived from, that I can learn about this.
And there you have your definition of SymmT immediately prior to Example 10 in your pdf.

You keep applying the transformation to the initial set and take the union of your results. In the case of a simple reflection, then you only need to apply the transformation once to obtain the final set. (Can you see why?) But if the transformation is, for example, a rotation of a quarter-turn clockwise around the origin, then you need to apply it 3 times. (Again, can you see why?)
 
  • #7
Ok, so ##Symm_T\left(A\right) =\bigcup_{k=0}^\infty T^k\left(A\right)##. Can you make progress now?
 

Related to Symmetry of a graph. SymmT(A)?

1. What is the definition of symmetry in a graph?

Symmetry in a graph refers to the property of a graph where there is a certain balance or similarity in its structure when it is reflected or rotated.

2. How can I determine if a graph is symmetric?

To determine if a graph is symmetric, you can use the SymmT(A) function. This function takes in a graph and checks if there is a symmetry present by comparing the graph to its reflected or rotated version.

3. What is the significance of symmetry in a graph?

Symmetry in a graph can provide important information about the relationships between the elements in the graph. It can also help in identifying patterns and making predictions about the behavior of the graph.

4. Are there different types of symmetry in a graph?

Yes, there are different types of symmetry in a graph. The most common types are reflection symmetry, rotational symmetry, and translational symmetry.

5. Can a graph have more than one type of symmetry?

Yes, a graph can have more than one type of symmetry. In fact, there are graphs that exhibit multiple types of symmetry, such as a square which has both reflection and rotational symmetry.

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