1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Snowflake question

  1. Jun 14, 2006 #1
    I have a question to do with Koch's snowflake and anti snowflake..
    I have no clue how to find the formula for the total area of each.
    This is my table for snowflake
    & this is it for anti-snowflake

    I've realised that the area for both are finite, with the snowflake being 81x(8/5) and antisnowflake being 81x(2/5)
  2. jcsd
  3. Jun 14, 2006 #2
    since you know how much area is added, you can set up a recurrence relation. for the snowflake, A_n = A_n-1 + 27*(4/9)^(n-1). since A_n-1 = An-2 + 27*(4/9)^(n-2) and so forth, A_n = A_0 + 27*(4/9)^(1-1) + 27*(4/9)^(2-1) + ... + 27*(4/9)^(n-1). this is a geometric series with the ratio 4/9<1 so it will converge as n goes to infinity.
    Last edited: Jun 14, 2006
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Snowflake question
  1. Limit question (Replies: 9)

  2. Function Question (Replies: 7)

  3. Combinatorics question (Replies: 4)

  4. Trig question (Replies: 16)