Lesson 7 of 11
What each stage really does
Show on a big screenPut a small bump on every side of a triangle. Then do it again on the new sides. The bump is an equilateral triangle, one with three equal sides. Start with sides 1 unit long. The outline is the length all the way around the shape.
Step 1 of 4
- One straight side, 1 unit long.
- Cut it into 3. Build a bump on the middle part.
- Do it again on each of the 4 pieces.
- The outline is 4/3 as long, every step.
Rule: Cut each side into 3 equal parts. Build an equilateral triangle on the middle part. Remove that middle part. Repeat on every new side.
| Step | Sides | Outline in units |
|---|---|---|
| 0 | 3 | 3 |
| 1 | 12 | 4 |
| 2 | 48 | 16/3 |
| 3 | 192 | 64/9 |
Every side becomes 4 sides. Each new side is 1/3 as long. Four new sides make 4 × 1/3 = 4/3 of one old side. So the outline grows 4/3 times each step. The shape this rule builds is the Koch snowflake.
Tap Run the rule. Watch the sides and the outline grow.
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Try the lab to finish this lesson.