Tetra Balloon Hats and Sierpinski Triangle Structures

Benji will show you the ins and outs of making a tetra balloon hat in this video. Download detailed instructions below!

### Why are they called Tetra Hats?

The name comes from the hat's 4 sides. The hat is an example of a shape called a tetrahedron, which uses the Greek roots for 4 ("tetra") and side or base ("hedron"). Do you see the 4 sides?

Level 0 Level 1 Level 2 Level 3 Level 4

### What is a Sierpinski triangle?

Benji's tetra hat is an example of a 3-D Level 0 Sierpinski triangle. A Sierpinski triangle follows an interesting pattern. We can categorize its "level" based on how many sizes of white, upside-down triangles are within it.

The Level 0 triangle (the same level as Benji's 3-D hat) has 0 sizes of white triangles in it, since it has 0 white triangles in it at all. The Level 1 triangle has 1 white triangle, so it has 1 size of triangle. The Level 2 has 2 different sizes of white triangles. The Level 3 has 3 different sizes of white triangles.

Q: How many sizes of white triangle are in the Level 4 triangle?

Challenge question: Can you predict how many white triangles will be in the Level 5 triangle?

Here's another way to explore Sierpinski triangles.

How many white triangles do they each have? How many more triangles does the red triangle have than the blue?

What's the relationship between the two numbers? Is there a pattern to how many white triangles are in each level? Do you see any similarities between the two triangles' shapes?

### What is a fractal?

A Level Infinity Sierpinski triangle is called a "fractal." When you zoom into a Sierpinski triangle fractal, you'll see infinite white triangles inside it. This means it will keep repeating itself as you zoom in further on it.

There are lots of cool fractals in the world, and many occur in nature. Try asking an adult to help show you more fractals online.

### Who was Sierpinski?

Wacław Sierpiński (1882-1969) was a Polish mathematician who explored many important and interesting topics in math, including set theory, number theory, and topology. He's best known today as the namesake of three fractals.