In this activity, students blow clusters of bubbles to explore the geometry of bubble structures.

Bubbles join in a way that requires the least amount of stretching, keeping a minimal surface structure. The patterns created by bubble clusters were first observed and written down by Belgian physicist Joseph Plateau in the 19th century, but you can recreate these patterns today using only a little bubble solution and a straw.

Two Bubbles
When two bubbles meet, they will join and share one common wall. If the bubbles are the same size the wall between them will be flat, because this uses the minimal surface area (this fact was actually just proven in 2000 and is called the Double Bubble Conjecture).

If the bubbles are different sizes, the smaller bubble pushes the wall and bulges into the larger bubble, because it has a higher internal pressure. See soapbubble.dk for more about air pressure in bubbles.

Three Bubbles
When three bubbles meet (even if they’re different sizes), three walls will form a Y shape. The angles between the bubble walls are always 120° (360° divided by 3).

More than Three Bubbles (on a flat surface)
As you add more bubbles to a cluster on a flat surface, they will rearrange themselves so that there are never more than three films in contact along an line or four films in contact at any one point. This creates multiple 120° angles in the shape of a Y.

A network of 120° angles creates a pattern of hexagons. Bees build honeycombs in the shape of hexagons for the same reason that bubbles build hexagons—it’s the way to make the most compartments with the least amount of “stuff” forming the walls.

More than Three Bubbles (in 3 dimensions)
You can only create clusters of more than three bubbles in 3 dimensions (e.g. free-floating bubbles, or bubbles hanging from a bubble wand).

Four bubbles will always form edges that meet at 109 degrees 29 minutes and 16 seconds. They will form a 3 dimensional Y shape called a tetrahedron.

Another way to think of this is that six bubble sheets meet at 109 degrees.

### Objectives

• Use their knowledge of soap films and minimal surface structures to make bubbles of various sizes, shapes, and arrangements.

### Materials

• Per Group:
1 small tub of All Purpose Bubble Solution

• Per Student or Pair of Students:
1 small bubble wand or straw
1 plastic plate or yogurt lid

### Key Questions

• What is different about the surface that two bubbles share versus the rest of their surface area?
• Why do two same-sized bubbles share a straight wall when they meet?
• Why does a smaller bubble bulge into a bigger bubble?
• What is special about the angle 120°?
• How do clusters of bubbles relate to bees?

### What To Do

Set Up

1. Demonstrate how to blow clusters of bubbles using either a small bubble wand or straw. Blow them gently, one by one, onto a plastic plate or clean surface that has been wetted slightly with bubble solution.
2. Make some initial observations about the surfaces where the bubbles connect, the way that bubbles connect and the angles that form between their shared surfaces.

Activity

1. Create bubble clusters on a plastic plate or other clean surface, individually or in pairs.
2. Observe the number of bubbles, the overall shape of the cluster and estimate of the angles where the bubbles join. You might see shapes that remind you of a peach, a turtle, a flower, or a honeycomb as more bubbles join the cluster.
3. Experiment with different sized bubbles as well as different numbers of bubbles within a cluster.
4. Observe any patterns with each cluster of bubbles. You will find that:
• One bubble is a sphere
• Two bubbles connect with a straight edge
• Three bubbles join at 120° angles
• Four free-hanging bubbles make a tetrahedral shape with angles at 109°
1. ​Note what happens when you make clusters of 4, 5 or more bubbles.

### Extensions

• Use a bubble wand and a straw to make 3-D bubble sculptures.
• What kinds of shapes can you make using different bubble sizes and arrangements?

### Other Resources

Science World | YouTube | Bubbles

Exploratorium | Soap bubbles

David A. Katz | The Chemistry (and a little bit of physics) of Soap Bubbles

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Artist: Jeff Kulak

Jeff is a senior graphic designer at Science World. His illustration work has been published in the Walrus, The National Post, Reader’s Digest and Chickadee Magazine. He loves to make music, ride bikes, and spend time in the forest.

Egg BB

Artist: Jeff Kulak

Jeff is a senior graphic designer at Science World. His illustration work has been published in the Walrus, The National Post, Reader’s Digest and Chickadee Magazine. He loves to make music, ride bikes, and spend time in the forest.

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Artist: Jeff Kulak

Jeff is a senior graphic designer at Science World. His illustration work has been published in the Walrus, The National Post, Reader’s Digest and Chickadee Magazine. He loves to make music, ride bikes, and spend time in the forest.

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Artist: Michelle Yong

Michelle is a designer with a focus on creating joyful digital experiences! She enjoys exploring the potential forms that an idea can express itself in and helping then take shape.

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Artist: Michelle Yong

Michelle is a designer with a focus on creating joyful digital experiences! She enjoys exploring the potential forms that an idea can express itself in and helping then take shape.

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Artist: Michelle Yong

Michelle is a designer with a focus on creating joyful digital experiences! She enjoys exploring the potential forms that an idea can express itself in and helping then take shape.

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Artist: Ty Dale

From Canada, Ty was born in Vancouver, British Columbia in 1993. From his chaotic workspace he draws in several different illustrative styles with thick outlines, bold colours and quirky-child like drawings. Ty distils the world around him into its basic geometry, prompting us to look at the mundane in a different way.

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Artist: Ty Dale

From Canada, Ty was born in Vancouver, British Columbia in 1993. From his chaotic workspace he draws in several different illustrative styles with thick outlines, bold colours and quirky-child like drawings. Ty distils the world around him into its basic geometry, prompting us to look at the mundane in a different way.