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Honey Bees and Geometry?

Because honey is so important it would make sense for bees to want to maximize the amount of honey they can fit in their hive. So, How can we maximize this volume?

Now take a few minutes to draw a random shape and try to fit other shapes to it to create a honey comb. What do you notice? Does this system seem complex or simple?

Bees need to consume 8 ounces of honey to make 1 ounce of wax. So, it would make sense for them to want the shape that requires the least amount of wax... or the smallest perimeter.

Take the next few minutes to investigate which shape, triangles, squares, or hexagons have the smallest perimeter.

Hexagons have the smallest perimeter, making them an ideal choice for bees.

What other properties of hexagons make them such a great shape for honey combs?

What do you notice when you compare the area of a hexagon to the area of other shapes?

Take a few minutes to investigate this relationship.

Hexagons also have the great area compared other shapes that do not produce gaps!

This allows bees to maximize the amount of honey they can fit into one cell.

Reflect on what you have learned to answer the questions bellow.

1. Name 4 reasons bees chose hexagons to make the cells of their honey combs over other shapes.

2. Describe how these reasons relate to geometry.

3. How effective would it be to have a random shape represent each cell? Explain your answer.

Thank you for participating

11/25/2013 @CMU Mount Pleasant MI

Inspiration for this activity came from

Krulwich, Robert. "What Is It About Bees And Hexagons?" NPR. NPR, n.d. Web. 25 Nov. 2013. http://www.npr.org/blogs/krulwich/2013/05/13/183704091/what-is-it-about-bees-and-hexagons

2,000 year old mystery

  • Why Hexagons?
  • Why not Triangles, or Squares?

Honey Bees ALWAYS make their honey combs out of PERFECT Hexagons.

  • All 6 sides are exactly the same length

Importance of Honey to Bees

  • Food
  • Creates wax
  • Holds hive together
  • Holds honey comb together

If we start with a random shape, like the one depicted bellow, we will have to keep customizing each additional shape to fit the others. Every shape will be different!

If bees did this they would have to work one by one... which would take a long time.

If all the cells were the same shape and size they can all work simultaneously... which is more efficient.

So honey comb cells are all the same size so that bees can work more efficiently....

But why Hexagons?....

Using shapes such as circles, pentagons, and octagons would cause gaps between cells. This would require extra patching, using more time and wax then necessary.

So why not chose triangles or squares? These shapes don't create gaps...

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