Ask Question
17 May, 15:41

Koch's kinky curve is created by starting with a straight segment and replacing it with four segments, each 1/3 as long as the original segment. So, at the second stage the curve has three bends. At the next stage, each segments replaced by four segments, and so on. How many bends does this curve have at the third stage? The fourth stage? The nth stage?

+2
Answers (1)
  1. 17 May, 16:29
    -1
    Stage # segments # bends

    1st stage 1 segment 1 - 1 = 0 bends

    2nd stage 4*1 segments 4 - 1 = 3 bends

    3rd stage 4*4 = 16 segments 16 - 1 = 15 bends

    The number of bends is equal to the number of segments less 1, becasuse two segments are required to make one bend.

    4th stage 4*4*4 = 64 segments 64 - 1 = 63 bends.

    nth stage 4^ (n-1) segments 4^ (n-1) - 1 bends
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “Koch's kinky curve is created by starting with a straight segment and replacing it with four segments, each 1/3 as long as the original ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers