# Symmetry in the world around us (Investigation)

Lesson

Hopefully by now you've already read about what symmetry is and how it is defined. If not, read here for a quick review. However, it is important to know that symmetry is by no means limited to what you find in your maths textbooks. Symmetry exists all around us, in both the built and the natural environment.

#### Symmetry in the Built Environment

The use of symmetry in buildings and objects is one of the most fundamental human traits. From ancient times to modern times and across all human cultures, symmetry has been used as a key design principle, as it is universally perceived as aesthetically pleasing.

For example, have a look at this photo of the Taj Mahal, followed by a top-down floor plan:

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Source: User Dhirad / Wikimedia Commons / Licensed under CC BY-SA 3.0

Source: User Vmoscarda / Wikimedia Commons / Public Domain

1. What kind of symmetry does the Taj Mahal display when viewed from the front?

2. What kind of symmetry does the Taj Mahal display when viewed from the top?

3. Try to find another ancient structure which displays symmetry, and describe what kind of symmetry it is.

4. Find an example of a major modern structure which displays symmetry , and describe what kind of symmetry it is.

5. Find an example of a major building from any era which does not display any kind of symmetry. See if you can draw what it would look like if it was made symmetrical in some way. Do you think this would look better or worse than the original?

6. Look through your pencil case to see how many objects you own display some kind of symmetry, and how many are completely asymmetrical.

6. Why do you think humans prefer symmetrical buildings and objects?

#### Symmetry in the Natural Environment

One theory of the reason that we prefer symmetrical objects and buildings is that we ourselves are symmetrical, or relatively.

According to this theory, the fundamental symmetry of the human body plan means that people who have obvious asymmetry in their bodies or faces are likely to be less genetically healthy, and that over time humans evolved to perceive symmetry as aesthetically pleasing so that they can pick the most genetically healthy mates.

1. What do you think of this theory? Can you think of other reasons that humans might prefer symmetrical buildings and objects?

Humans and all other mammals exhibit left-right symmetry, but there are examples of organisms which have different symmetry, or none at all. Have a look at the following organisms, and comment on their symmetry (if any):

Source: Paul Shaffner / Wikimedia Commons / CC BY 2.0

Source: Jason Pratt / Flickr / CC BY 2.0

Source: Gregory Phillips / Wikimedia Commons / CC BY-SA 3.0

Source: Wikimedia commons / CC BY 2.5

2. In most of the examples of symmetry in architecture, you will notice that the most prominent form of symmetry is left-right, just like our bodies. Do you think that buildings would like different if a starfish built them? See if you can draw an architectural design that might appeal to a starfish.

3. Why do you think symmetry is so common in the body plans of living things?

#### Find Something Symmetrical

Symmetry is everywhere, and once you go looking for it you will see it everywhere. See if you can find some symmetrical objects, and take photos to share with your class! You can use a digital camera or smartphone to complete the following questions:

1. Take a photo of a symmetrical object from the built environment. What kind of symmetry does it have?

2. Draw a picture of what the object would look like if it was asymmetrical. Do you think it looks better when it is symmetrical or asymmetrical?

3. Draw a picture of what the object would look like if it had a different kind of symmetry. Comment on the type of symmetry in your drawing.

4. Take a photo of a symmetrical object from the natural environment.

5. Draw a picture of what the object would look like if it was asymmetrical. Do you think it looks better when it is symmetrical or asymmetrical?

6. Draw a picture of what the object would look like if it had a different kind of symmetry. Comment on the type of symmetry in your drawing.