• Honeycombs and Hot Dogs

    by  • May 18, 2013 • Math • 0 Comments

    14 CirclesI came across this NPR article by Robert Krulwich, called “What Is It About Bees And Hexagons?,” and I got totally sucked in to the comment thread. The more I read, the cooler it seemed, and the more I wanted to build these things and teach my kids about them. Each cell starts out looking something like half of a hotdog – cylindrical with a hemispherical bottom. The bees build these with amazing regularity of spacing, working out from one and surrounding it with others, like in this image.

    Honeycomb with circlesHoneycomb Hex

     

    The heat of their bodies and the heat of the sun cause the wax to deform, and the six points of tangency around each circle become the six sides of the hexagonal cells that we recognize.

     

     

    Hotdog2 Hotdog1

     
     
     

    As cool as that is, the 3D is even cooler. As a demonstration of what happens, I tried to think like a 14-year-old and came up with this! Gross, but convincing. Yup, vacuum-packed hotdog halves -yum!

     

    The geometric shape that models this is a hexagonal prism with a rhombic pyramidal base. I made a net for it and have started to build a honeycomb.

    front back

    What’s really cool is that the bees build the layers back to back, staggered to fit into each other.

    I think this would make an awesome lesson – or geeky craft project!

     

     

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    About

    After teaching for 14 years, I now design curriculum and create digital and print instructional materials for high school and middle school math. I have also invented and am now marketing radian-scale protractors. Check out www.proradian.net! I'm very happily married and have 2 grown sons and a cat named Louie.

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