1. BUZZ INTO SHAPES BY MICHELLE HILL

2. What is a polygon? A closed plane figure that is made up of three or more line segments. For example:

3. What is a regular polygon? A polygon which is equiangular (all angles are equal in measure) and equilateral (all sides have the same length). For example:

4. A tessellation is created when a shape is repeated, covering a plane without any gaps or overlaps. The triangle, square and hexagon are the only regular polygons that can be tessellated.

5. Have you ever stopped to consider how many polygons can be found in nature? Core of a kiwiGiraffe’s body Bee Hive

6. Bees have not studied tessellations. Mother nature has instilled in the bee the instincts to use the least expenditure of energy and materials. They know that the square, the triangle and the hexagon are the only three self-tessellating regular polygons. But why the hexagon and not the triangle or square?

7. Let’s explore the volume of the three regular polygons that can be tessellated. Where A is the area of the base and H is the height of the prism. Triangle-Square- Hexagon- The formula for finding the volume of any polygon is: V=A x H ½ × length × width × heightS² × height 2.598076211 × 2 × height

8. Minding Your Own Beeswax 1.If you were building a honeycomb, would you want it to have gaps? Why, or why not? 2. Consider the three prisms: (A) (B) (C) If each shape has the same depth, which prism will hold the most honey? 3. Make a conjecture and provide a rationale, explaining why your choice of shape would hold the most honey. 4.Find the volume of each prism. (Remember that the depth is 1 unit.) ASSIGNMENT

9. After completing the assignment, you should have concluded that the hexagonal prism can hold more volume than the triangular or square prisms. Of the three, the hexagon has the smallest perimeter for a given area. This allows them to use less wax and do less work to enclose the same space. This is why the bee uses the hexagon!!!!

10. Additional Websites www.bushfarms.com/beesmath.htm http://ag.arizona.edu/pubs/insects/ahb/lsn34.html http://www.sde.idaho.gov/site/cnp/nutritionResources/fom Posters/ActivitySheet/2009-2010/honeyAS.pdf References www.google.comwww.google.com (google images)

11. A SPECIAL THANK YOU TO: Wanetta Thompson and Georgia Dahlgren Dr. Avard, Dr. Eggleton, Dr. Patton, Dr. Ludrick, Dr. Wood and Mrs. Dixon State Department of Education Sherry Howe and Dickson Public Schools Cameron University Wichita Mountain NWR & Staff