Nature and Geometry

What are these mysterious structures? Are these pieces of plastic packaging for mailing things? Are these parts of an air conditioning filter? Are these chunks of an old mattress? Nope. They are not even man made.

These are pieces of a Paper Wasp nest. Usually, a wasp nest can be found hanging from a tree, or under the eaves of a roof. A nest must have fallen to the ground and broken. Guess who brought these pieces to its home? A squirrel :) I found these pieces and other chunks of wood and leaves and dirt clods outside a hole in the ground. This hole in the ground was an entrance to a squirrel home. We'll talk about that some other time.

Paper Wasps sort of look like bees, but they are longer than bees. Paper Wasps are insects that chew up pieces of old wood and make spit wads. Oooh, ick, I know. But then they turn these "spit wads" into perfectly formed hexagonal cells.

Have you learned about hexagons? Hexagons are shapes that have six sides. Using, a ruler, try to draw a hexagon that has all the angles the same and all of the sides the same. It's pretty difficult. But now try to draw a hexagon without using a ruler. How does it look? Are the sides wiggly and different lengths? Are the angles all different?

Now take a look again at the Paper Wasp nest cells. These tiny compartments fit together perfectly! And a wasp has no rulers or any other measuring devices. It just KNOWS how to make these cells. Amazing! The cells are used as growing spaces for wasp eggs. The queen wasp will lay one egg in each cell. The egg will slowly change into a wasp.

These cells are made of hexagons that have "rotational symmetry." What that means is that if you turned (rotated) this hexagon around its middle, it would look the same no matter how you turned it. Snowflakes have rotational symmetry. If you turned a snowflake around its middle, it would be the same shape. What other items in nature have rotational symmetry? Flowers? Some of them, yes. What else? Try to think of a couple more.

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