This was the fourth Investigation of the LabLearner CELL Science and Art. In it, students continued the exploration of perspective and the illusion of depth in paintings. In addition, students studied symmetry and its use in art.

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A. Begin this part of the Investigation by encouraging students to summarize their activities in the Lab. Prompt student discussion by posing the following questions:

1. Ask students: What were the main questions we wanted to investigate in this lab? Students should indicate that the questions were: Is the human face bilaterally or radially symmetrical? Is a 200g mass bilaterally or radially symmetrical? How many planes of symmetry do objects have? Are they bilaterally or radially symmetrical? How does your perspective affect the appearance of an object?

2. Ask students: How would you summarize the types of experiments that you performed to investigate this question? Students should indicate that they performed three Trials. In all three Trials, they used a mirror to find planes of symmetry. In each Trial, they placed the mirror along several different planes and then looked at the image formed by the reflection in the mirror and the other half of the object. If the image appeared “normal,” then the plane was a plane of symmetry. Objects that had many planes of symmetry were classified as radially symmetrical. Objects that had only one plane of symmetry were bilaterally symmetrical.

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B. Begin analysis of the experiment by encouraging students to review their data from Trial 1.

Ask students: Is the human face bilaterally or radially symmetrical? Why? Bilaterally symmetrical.

a. Use this slide to walk students through the results from the experiment.

b. Discuss how only one of the planes tested – from the top of the head to the chin – produced an image that looked like the face. This was the only plane of symmetry.

c. All of the other planes produced images that were different from a “real” face.  Because the face only had one plane of symmetry, it was bilaterally symmetrical.

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2. Direct students to locate Problem 4 in their Student Data Record.

Ask students: Was the 200 g mass radially or bilaterally symmetrical? Why? Radially symmetrical.

a. Use this slide to walk students through the results from the experiment.

b. Discuss how each plane tested produced an image that looked like the intact 200 g mass.  As a result, the 200 g mass can be classified as an object with radial symmetry.

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3. Ask students: How does the number of planes of symmetry determine the type of symmetry? Students should indicate that if an object has more than one plane of symmetry is likely to be radially symmetrical. If it has ONLY ONE plane of symmetry, it is a bilaterally symmetrical object.

4. Direct students to look at Table A:

Ask students: Which objects were radially symmetrical?  Which objects were bilaterally symmetrical? Why?

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5. Encourage students to think about their results. 

Ask students: Can you think of any features the radially symmetrical objects had in common? Students should indicate that all of the objects they tested in the lab that were radially symmetrical were either circular or cylindrical in shape.

NOTE: Cylindrical and circular objects generally exhibit radial symmetry.  However, this conclusion may lead students to believe that only cylindrical and circular objects have radial symmetry.  Should this question arise, students may be interested to know that objects that have other shapes, such as a cube, would also be considered radially symmetrical because they possess many planes of symmetry. This slide shows other examples.

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Ask students: Describe your conclusions about objects that have bilateral and radial symmetry.  Use the following words or phrases in your description: Sample answers:

Objects that have more than one plane of symmetry are radially symmetrical. These objects are similar in that they are often circular or cylindrical.   

Objects that have only ONE plane of symmetry are bilaterally symmetrical. These objects are generally not cylindrical or circular in shape. 

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C. Provide an opportunity for students to extend what they have learned about symmetry.

1. Encourage students to recall the drawing they completed in the PreLab.

Ask students:  Does your drawing have symmetry? Student answers will vary depending on their drawing.  Accept all reasonable answers that students can support.  For example, some students may indicate that their drawings are not bilaterally or radially symmetrical because even if a plane is placed in the middle of the road, the two halves of the drawings are not mirror images of each other.  Other students may suggest that in artwork, symmetry may not be defined as parts of a painting as mirror images but rather that there is a balance in the number and size of the objects between two halves of a painting.  Therefore, they may suggest that their drawing is symmetrical because it contains a house and tree on both sides of the road.

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Before finishing this PostLab, consider a term we have used often during Investigation Four, “mirror image.” For example, we say our hands are mirror images of each other. You can see this by placing the palm of your hand on a mirror, as in the picture on the left of this slide. You can mimic this mirror image without a mirror by placing your two palms together.

However, a mirror image does not make two objects identical. In science, specific molecules that are perfect mirror images of each other can have very different properties. For example, the mirror image of the molecule that gives spearmint its distinctive smell and flavor gives caraway its distinctive smell and flavor.

To demonstrate the different properties of our right and left hands, try to shake someone’s right hand with your left. Also, try as you may, you will never be able to shake your own hand properly… try it!

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The following slides are designed to help students understand that symmetry may be defined differently by the fields of science and art. The concept of symmetry – the balance between parts of a whole – is the same.  However, science tends to have more strict parameters for symmetry in that the parts are mirror images of one another. 

Because artwork tends to portray or represent a myriad of events, ideas and emotions, symmetry is defined by how the elements within an artwork compare to one another.

This slide is an excellent example of bilateral symmetry in art. Notice that, even though there is clearly an overall bilateral symmetry centered on the vertical axis at the middle of the painting, the left and right side of the work are not identical – that is, they are not mirror images.

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In this slide, we have taken the left half of the School of Athens from the previous slide and created an exact mirror image.

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This slide directly compares Raphael’s original School of Athens to an actual mirror image of the left side of the painting (from the previous two slides). Notice that while there are many differences between the two images, the overall structure and “feel” is very similar due to the bilateral symmetry.

Thus, an artwork needn’t represent a precise mirror image to be considered bilaterally symmetrical.

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Another primary type of symmetry we have explored in this Investigation is radial symmetry. Remember that radially symmetric objects have more than one plane of symmetry and are often (but not always) associated with spherical, circular, and cylindrical objects.

There is perhaps no clearer example of radial symmetry in art than the Northern rose window of the Notre-Dame cathedral in Paris, France shown on this slide.

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Leonardo da Vinci’s classic painting, Last Supper, is another example of symmetrical balance, even though the left and right halves are not mirror images of each other. The central focus of the painting is Jesus, with the apostles equally divided on either side of him. Notice that there are actually two groups of three apostles, each on both sides of the center.

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Notice that while bilateral symmetry exists in both paintings, neither are exact mirror images.

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Balance doesn’t always mean symmetrical.  Sometimes artists use the word balance when referring to the “feeling” of harmony for a work of art overall.   In this case, the balance is often produced by asymmetry. 

The placement of objects in the painting are not symmetrical.  However, their location produces a sense of balance for the overall painting.  

Van Gogh’s Starry Night can be thought of as an example of asymmetrical balance.  (Although some people may describe this painting as having no balance– simply asymmetry– and therefore a feeling of drama.)  No apparent line divides the painting into left and right sides.  The large structure on the left is not balanced by an equally large structure on the right.  However, many see the larger mountains and moon on the right as a balance for the large structure on the left.

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The picture of sunflowers is sometimes described as asymmetrically balanced because the painting has no central focus. Yet, the structures on the left and right sides balance each other. As with many other aspects of art, some may see this painting as symmetrically balanced because one can imagine a dividing line down the middle of the painting with an equal number of objects on either side. This painting is presented as a less obvious choice for asymmetrical balance to emphasize the sometimes interpretive nature of art.

The scenic picture is a classic example of asymmetric balance, as the tall trees and animals on the right are not balanced by trees or animals on the left. In addition, there is no central point of focus in the painting. Nonetheless, a certain degree of symmetry is achieved by balancing the trees and animals on the right with the dark clouds and their shadows on the ground on the left.