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World 5 · The Koch Snowflake · 14 min · PRO

Sierpinski: when volume vanishes

Triangles with no area, the chaos game, and a pyramid with no volume

PRO · Symmetry & Fractals

World 5: The Koch Snowflake is part of PRO

The first world of Symmetry & Fractals is free. PRO opens the other 24 lessons in 6 worlds — simulations, quizzes and all.

  • Self-similarity and iteration
  • The perimeter that runs away
  • The area that stays finite
  • What does dimension mean?
  • Koch, Sierpinski, Menger: non-integer dimensions
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  • Practice exams and certificates

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