If you have ever tried to hang a picture and not been able to tell which end was up, then your picture might have had rotational symmetry. Rotational symmetry is the characteristic that makes an object look the same even after you've rotated it.
What is Rotational Symmetry?
The recycling icon is a very common symbol, and like most effective icons, the image itself is suggestive of its meaning. The arrows of the image appear to be moving in a circular manner, suggesting the circular concept of recycling. Adding to this perception is that if you were to rotate the image 120 degrees, and another 120 degrees, and a third 120 degrees, it would look the same at all three stops.
This attribute is called rotational symmetry. Many shapes have rotational symmetry, such as rectangles, squares, circles, and all regular polygons. Choose an object and rotate it up to 180 degrees around its center. If at any point the object appears exactly like it did before the rotation, then the object has rotational symmetry. In this lesson, you will be given several image examples, as well as definitions of the relevant concepts center, order, and degree of rotation.
What is the Center of an Object?
The center of a shape or object with rotational symmetry is the point around which the rotation occurs. If one was to spin a basketball on the tip of his finger, the tip of his finger would be the center of the rotational symmetry. If an object has rotational symmetry, its center will also be its center of balance.
Order of Symmetry
The order of symmetry - or for short, order - is the number of times an object or shape can be rotated and still look like it did before rotation began. Let's look at some examples.
Rotational symmetry with 180 degrees of rotation
Here we have a hexagon. It has an order of 2. Let's look at another example.
Rotational symmetry with two rotations of 72 degrees
Rotational symmetry with 72 degrees of rotation
Both the blue and orange shape and starfish have an order of 5 because you can turn them 5 times and they still look the same as they did before they were rotated.
Let's look at one more example.
Rotational symmetry with 120 degrees rotation
This one has an order of 3.
The smallest order would be an order of 2. You cannot have a shape or object that has an order of 1. An order of 1 would mean that you can complete a full rotation without it appearing as it did before the rotation. In other words, an order of 1 would mean that is has no rotational symmetry.
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The degree of rotation is the number of degrees required to rotate the shape or object so that it appears as it did before the rotation. A full rotation requires 360 degrees. To find the degree of rotation, you would divide 360 degrees by the order. Since 2 is the smallest order possible, then 180 is the largest degree of rotation possible.
Let's look back at the hexagon example. It has an order of 2, because it can be turned twice and look the same as it did when we started; so to find out the degree of rotation, we would take 360 (the number of degrees required in a full rotation) and we divide by 2 (the order of symmetry).
360 / 2 = 180
So, the degree of rotation is 180.
Common degrees of rotation are: 180 degrees (order 2); 120 degrees (order 3); 90 degrees (order 4); 72 degrees (order 5); and 60 degrees (order 6). Other, smaller degrees of rotation are possible but rare.
An object has rotational symmetry if you can rotate the image around the center and it appears just as it did before the rotation. The number of times that it can be rotated is called the order of symmetry. The degree of rotation equals 360 degrees divided by the order of rotation, and will range between 0 and 180 degrees.
Aspects of Rotational Symmetry
Center of an Object
Order of Symmetry
Degree of Rotation
The center about which an object is rotated
*The number of times an object can be rotated and still look like the original object * Can't be less than 2
*The number of degrees required to rotate the object so that it appears the same as it did before the rotation *360 degrees divided by the order of rotation
When you are finished, you should be able to:
Describe rotational symmetry
Explain what the order of symmetry and the degree of rotation are and how they are connected
In this creative project, students will create a work of art that has rotational symmetry. Students can use any medium they desire, such as clay, paint, colored pencils, or collage. However, the art that students create should have rotational symmetry and be able to be hung in any direction, as described in the lesson. For example, students might create a mandala like shape from cut outs of colored paper in a color scheme they enjoy. This would be an example of rotational symmetry.
Now that you understand what rotational symmetry is and how to identify it, it's time to try your own hand at creating something with this type of symmetry. In this creative assignment you will be creating a work of art that has rotational symmetry. You can choose any medium to work with, such as paint, clay, collage, or something else of your choosing. However, your end product should have rotational symmetry. For a list of constraints, see the criteria for success below.
Criteria For Success
Art should have rotational symmetry
Art should include a color scheme that is attractive
The student should be able to discuss their vision for the piece and explain why it has rotational symmetry
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