Ahhhh Isnt symmetry wonderful Symmetry is all around us Its in our art nature and even ourselves It has been proven that we find things with symmetry more pretty So in order to have prettier math we should learn about it dont you think ID: 309450
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SymmetryAhhhh. Isn't symmetry wonderful?Symmetry is all around us. It's in our art, nature and even ourselves. It has been proven that we find things with symmetry more pretty. So in order to have prettier math, we should learn about it, don't you think.The following slides will teach you about Reflection, Rotational, and Translational symmetry.
Reflection
Rotation
TranslationSlide2
Reflection SymmetryIn our first type of symmetry, I will show you Reflection Symmetry. Reflection symmetry is also called line or mirror symmetry. Like all other types of symmetry,as you will soon learn, reflection symmetry can occur either inside or outside of the figure. Confused? Don't be.
Take a look at the shape to the left. It has many lines of reflection symmetry. "What is this 'line of symmetry' of which you speak?" Thank you for asking.
If you made a line through the figure, then fold over that line, the two halves of the shape would fit like a peanut butter sandwich.See how the two halves of the shape look the same? They have reflection.
"But wait! You said that there was reflection outside of shapes. You've only shown reflection inside of a shape."
Very observant. There's hope for you yet.
Here we have a humble triangle.
We can reflect it easily.
Imagine that the line is a mirror. The image on the
right is the reflection. Cool, huh?
line of symmetry
If you want to try and see if this works, click on the shape. Then, go up to the little grey arrow and click on it. Make a copy and then click on that shapes little grey arrow and then click on flip. Now lay that shape on top of the original. The two shapes will line up exactly if the shape is laid down correctly. This is shows how both sides on the line of symmetry are the same.Slide3
Rotational SymmetryRotation symmetry is all around us. Around and around and around. "Colleen, what are you babbling about? Get to the point."Okay. What I'm babbling about is circles! Specifically, hubcaps. Hubcaps are great examples are rotational symmetry. Look
"Um... Colleen? That hubcap doesn't have symmetry."(Sigh) Yes it does. While it may not have reflectional symmetry, it does have rotational symmetry.
"Oh yeah?"Yeah."Well prove it!"Okay, I think I will.
Okay, see that faded out picture of the hubcap?"Yes..."Click on the hubcap and drag it on top of the other picture. Is it a perfect fit?"Yes..."Now click on the faded out picture and pull the green circle. See how you can turn the picture around?"Yes..."
Now turn the picture 90 degrees counter clockwise (the little green circle will be on the left now). Does the hubcap (don't look at the words on the tire, just look at the design of the hubcap) overlap perfectly?"..."Well...?"Yes."Thank you
Now over to your right is an example of
rotational symmetry outside of the shape.
These two objects are on a grid. The white
triangle is the original one. The red one is
a 180 degree rotation around the origin.
With other rotations, for example, 90 degrees
counterclockwise around the origin, the key wordis counterclockwise. You need to say that when youare talking about the rotation, except for if its rotated180 degrees because that is the same clockwise as
counterclockwise. With all types of rotational symmetry, both inside and out, you have to give thedegree of rotation, or how far it has to be rotated for
the shape to look exactly the same again.Slide4
Translational SymmetryHey, you know how wallpaper has a repeated pattern? Well guess what? That is sy..."No."What?
"No. You are not about to tell us that that is symmetry. It isn't."Oh but it is! Do I have to demonstrate?"Here we go again."
This specific type of symmetry is called Translation Symmetry. For it to be translation symmetry, the shape has to be the exact same (This is where SMART notebook comes in handy).
With translation symmetry, the shape is slid. You can slide it up, down, to the left, or right, or a combination there of.
In this pattern, there are two distinct parts, the diamonds and the squares. The squares are moved one unit down and one unit to the right. The diamonds are moved one unit to the right and then up one unit. Then the pattern starts from the beginning again.
square
diamond
a
b
c
This is a translation on a xy grid.
The initial figure triangle abc is drawn on the
grid. The second figure, the translation of it
is moved three units down and three units to
the right. The new triangle is called a prime,
b prime, c prime.
When a question says (x + 3, y + 3) it really
means that each vector needs to have 3 added
on the x axis and 3 added on the y axis.
a prime
b prime
c primeSlide5
Questions1. How did using SMART Notebook software and camera help me create designs with symmetry?
SMART Notebook software helped me with creating designs with symmetry by being able to clone a shape and thusly get an exact replica of the original shape. I didn't use the camera.2. How did using technology impact your understanding of the mathematics and your productivity?
The technology greatly increased my productivity by, instead of having to wait for the whole class or a partner to move on, by having my own computer, I was able to work at my own pace. I don't think that the technology necessarily helped my understanding of the mathematics because I already understood the math well enough to be able to make a SMART Notebook document about it.