Snowflakes - Netflix

Type: Scripted

Languages: Korean

Status: Ended

Runtime: 60 minutes

Premier: 2000-11-13

Snowflakes - Koch snowflake - Netflix

The Koch snowflake (also known as the Koch curve, Koch star, or Koch island) is a mathematical curve and one of the earliest fractal curves to have been described. It is based on the Koch curve, which appeared in a 1904 paper titled “On a continuous curve without tangents, constructible from elementary geometry” (original French title: Sur une courbe continue sans tangente, obtenue par une construction géométrique élémentaire) by the Swedish mathematician Helge von Koch. The progression for the area of the snowflake converges to 8/5 times the area of the original triangle, while the progression for the snowflake's perimeter diverges to infinity. Consequently, the snowflake has a finite area bounded by an infinitely long line.

Snowflakes - Variants of the Koch curve - Netflix

which approaches infinity as n increases.

A                      n                          =                              1            5                          +                              4            5                                    ∑                      k            =            0                                n                                                (                                          5                9                                      )                                k                                                        giving                                            lim                      n            →            ∞                                    A                      n                          =        2                ,              {\displaystyle A_{n}={\frac {1}{5}}+{\frac {4}{5}}\sum {k=0}^{n}\left({\frac {5}{9}}\right)^{k}\quad {\mbox{giving}}\quad \lim A_{n}=2\,,}  

Snowflakes - References - Netflix