In this video segment from Cyberchase, Bianca wants to learn why her plants keep dying, so she transports them in a carriage to the New York Botanical Garden. A helpful plant expert shows her some patterns in plants, including bilateral and rotational symmetry, before discovering the pattern that may be killing Bianca's plants.
Symmetry can be found all around us. You need only look in the mirror to find evidence that the human body is symmetrical. If you draw a line down the middle of your body, you will see that one side is the mirror image of the other side: two eyes, two ears, two arms, two legs, ten fingers, etc.
The type of symmetry first mentioned in the video segment is called bilateral symmetry, which is also called reflection symmetry or mirror symmetry. A figure has bilateral symmetry if you can draw a vertical or horizontal line through the middle of the figure and one half of the figure is a mirror image of the other half. The line down the middle is called a line of symmetry. In the video segment, the first leaf shown by the plant expert exhibits bilateral symmetry.
Another common type of symmetry is rotational symmetry. If a figure can be rotated a certain number of degrees about its center and look exactly the same, the figure is said to have rotational symmetry. The angle through which the figure can be rotated to make it look the same is called the angle of rotation. For example, the five-pointed star can be rotated 72 degrees about its center, and it will look exactly as it did in its original position. An equilateral triangle, which has sides of equal length, can be rotated 120 degrees about its center and it will still look the same. Many objects in nature, such as some flowers and snowflakes, exhibit rotational symmetry. In the video segment, the flowers that exhibit rotational symmetry all had five petals, which means that their angle of rotation would be 360/5 degrees, or 72 degrees.
Plants and animals that generally exhibit symmetrical features are thought to be healthier than asymmetrical members of their species. Scientists believe that humans and animals inherently associate symmetrical features with a strong immune system, which is seen as a likely predictor of strong and healthy offspring. Researchers have found that animals and humans often seek out mates with symmetrical features.
In addition to nature, symmetry exists in many man-made objects and is an important concept in art, science, and architecture. When choosing their brand logos, companies have taken advantage of the fact that the human eye is attracted to symmetry. If you think about some of the sports team and company logos you know, you may recognize that many of them exhibit bilateral or rotational symmetry.
To learn about the symmetry found in snowflakes, check out Snowflake Physics Flash Interactive.
Bianca: I'd give anything for a green thumb. No matter how hard I try I kill every plant I own... it's a pattern, one that I need to break. You've heard about homicide? I'm guilty of herbicide! I water my plants every day. There's something wrong. I need help from an expert. (It's okay sweeties, we're gonna get you some water).
This is amazing; so many gorgeous plants! And none of them are dead. Can you help me? I have an emergency.
Gwen: Should I call an ambulance?
Bianca: Well, not that kind of emergency. I’m a plant killer, and I want to change.
Gwen: What do you mean?
Bianca: I mean, I want to learn more about plants, so that they can live long and prosper.
Gwen : I’d be happy to help. How about if I show you around the garden?
Bianca: That would be great! It’s amazing to see so many different kinds.
Gwen: It’s also interesting to see what they have in common. Notice anything?
Bianca: Yeah, they’re not brown, like mine.
Gwen: Anything else? Here’s a hint – look at the leaves.
Bianca: Hmmm. On each leaf, the right side looks like the left side.
Gwen: Right. And if you fold this down the middle, both sides match up. Many leaves are symmetrical. Symmetry is just one of the patterns found in nature.
Bianca: Wow, these flowers are symmetrical, too! The right side looks like the left side.
Gwen: Right. But if I also rotate the flower just the right amount…
Bianca: …it looks like it did before you rotated it.
Gwen: That pattern is called rotational symmetry.
Bianca: Wow! These flowers have rotational symmetry, too. Why do plants have symmetry?
Gwen: No one knows for sure. But scientists think it helps the plant get the sun and nutrients it needs to grow. Symmetry also may help plants stay balanced, so they don’t fall over.
Bianca: I just noticed something else. Every one of those purple flowers has five petals.
Gwen: You just found another pattern! It so happens that lots of different flowers have five petals.
Bianca: Like those yellow ones!
Bianca: And those pink ones!
Bianca: Like the plants, my symmetrical brain needs some nutrients. Do you want an apple?
Gwen: Yes, thank you. I’d like to show you something.
Bianca: Awesome! A star is born!
Gwen: Every apple blossom turns into an apple with five seed compartments.
Bianca: Every apple?
Gwen: Yup. Guess how many petals an apple blossom has?
Gwen: You got it.
Bianca: That is so cool! I know a lot more about plants than I did before. But I still don’t know how to keep mine alive. I water them every day.
Gwen: Every day?
Bianca: Right before breakfast.
Gwen: I think we just uncovered another pattern. You water your plants every day. You’re probably over watering them. You’re killing them with kindness!
Bianca: How is that possible?
Gwen: When you over water, the soil gets so soggy that oxygen can’t reach the roots. Then the roots rot and the plant dies.
Bianca: That’s great news!
Gwen: It is?
Bianca: Yeah, because all I have to do is change my pattern and water them less frequently, and they’ll live. I can have a green thumb!
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