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Just Alike: What is Radial Symmetry?

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Author: Janice VanCleave

Problem

What is radial symmetry?

Materials

  • Sheet of dark-colored construction paper
  • 3-by-5-inch (7.5-by-12.5-cm) index card
  • Pencil
  • Scissors

Procedure

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  1. Fold the paper in half twice.
  2. Along the short end on the righthand side of the index card, draw the pattern shown in the diagram.
  3. Cut out the pattern.
  4. Lay the pattern on the colored paper so that the longest edge of the pattern is on one of the folds and the shortest edge of the pattern is on the other fold.
  5. Outline the pattern on the paper.
  6. Turn the design over and lay it on the adjacent (neighboring) folded edge. Outline the pattern on the paper.
  7. Cut out the figure drawn on the paper, cutting through all four layers of paper. Do not cut along the lines in the corner, as indicated by the solid lines in the diagram.
  8. Keep the cutout figure and discard the rest of the paper.
  9. Unfold the figure and draw two diagonal lines across the center of the figure.
  10. Study the figure and determine how many identical parts it has.

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Results

The figure has four identical parts spreading out from its center.

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Why?

The four parts of the figure have balanced proportions, which means that they are all the same size, shape, and distance from each other. A figure that has balanced proportions is said to have symmetry. Each part radiates (spreads out) from the center of the figure in a repeating pattern like the spokes on a wheel. This is a type of symmetry called radial symmetry.

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Let's Explore

Would the figure have radial symmetry if 2 different patterns were used? Repeat the original experiment, using 2 different patterns, such as the ones shown. Remember, if a figure has a repeating pattern that radiates from the center, even if the pattern repeats only once, the figure has radial symmetry.

Show Time!

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  1. Figures have bilateral symmetry if, when the figure is folded on a line, the two halves are identical. The line between the two halves is called a line of symmetry. How many lines of symmetry are in the figure you made in the original experiment? Science Fair Hint: Make a diagram showing each line of symmetry in the figure. Number each of the lines. NOTE: The figure has four lines of symmetry.
  2. Figures with radial symmetry also have rotational symmetry. Rotational symmetry means that one of the repeating patterns will fit into another when the figure is rotated a certain number of degrees. Demonstrate rotational symmetry by using the figure from the original experiment. Place the figure in the center of a sheet of typing paper so that the figure's straight outer edges are parallel to the edges of the paper. Draw an outline of the figure on the paper. Lay the drawing on a piece of thick cardboard about the same size as the paper, and secure the paper to the cardboard with tape. Label the four straight outer lines of the drawing 0°, 90°, 180°, and 270° as shown. Place the figure on top of the drawing, and stick a pushpin through the center of the figure, the drawing, and the cardboard. Make a mark on one of the figure's repeating patterns, then rotate the figure and find all the possible degrees at which the figure and the drawing overlap. Display this model of rotational symmetry and use it in an oral explanation of this symmetry.
  3. Nature provides many examples of bilateral and radial symmetry. The flowers of orchids, snapdragons, and sweet peas have bilateral symmetry. Flowers such as roses, wild geraniums, and morning glories have radial symmetry. Study the symmetry of these and other flowers. Use photographs of flowers to prepare posters representing both types of symmetry.
    1. An apple can be used to represent bilateral symmetry. Ask an adult to cut an apple in half from top to bottom. Make a print of one half of the apple halves. Cover a paper plate with tempera paint. Rub the cut side of the apple half in the paint and then press it on a sheet of white paper. Allow the paint to dry. Look for a line of symmetry on the print. Test what appears to be a line of symmetry by folding the print in half along the line.
    2. An apple can also be used to represent radial symmetry. Ask your adult helper to cut another apple across the middle. Make a print with one of the halves as before. Label the type of symmetry represented and display the print with the other one.

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Check it Out!

Point symmetry is a special type of rotational symmetry. Use a geometry text to find out more about point symmetry. Does a figure with point symmetry have bilateral symmetry? Show examples of this type of symmetry.

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