Number of Iterations of Koch Curve given Length after n Iterations Calculator

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✖The Length of Koch Curve after n Iterations is the length of Koch Curve after completing n number of iterations on the original or initial length.ⓘ Length of Koch Curve after n Iterations [l_n]			+10% -10%
✖The Initial Length of Koch Curve is the length of the curve which undergoing iteration to form the Koch Curve of respective iteration order.ⓘ Initial Length of Koch Curve [l₀]			+10% -10%

✖The Number of Iterations of Koch Curve is the number of steps completed during the process of iteration in the formation of Koch Curve.ⓘ Number of Iterations of Koch Curve given Length after n Iterations [n]

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Formula

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Number of Iterations of Koch Curve given Length after n Iterations

Formula

`"n" = (ln("l"_{"n"}/"l"_{"0"}))/(ln(4/3))`

Example

`"3"=(ln("64m"/"27m"))/(ln(4/3))`

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Number of Iterations of Koch Curve given Length after n Iterations Solution

STEP 0: Pre-Calculation Summary

Formula Used

Number of Iterations of Koch Curve = (ln(Length of Koch Curve after n Iterations/Initial Length of Koch Curve))/(ln(4/3))
n = (ln(l_n/l₀))/(ln(4/3))
This formula uses 1 Functions, 3 Variables

Functions Used

ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., ln(Number)

Variables Used

Number of Iterations of Koch Curve - The Number of Iterations of Koch Curve is the number of steps completed during the process of iteration in the formation of Koch Curve.
Length of Koch Curve after n Iterations - (Measured in Meter) - The Length of Koch Curve after n Iterations is the length of Koch Curve after completing n number of iterations on the original or initial length.
Initial Length of Koch Curve - (Measured in Meter) - The Initial Length of Koch Curve is the length of the curve which undergoing iteration to form the Koch Curve of respective iteration order.

STEP 1: Convert Input(s) to Base Unit

Length of Koch Curve after n Iterations: 64 Meter --> 64 Meter No Conversion Required
Initial Length of Koch Curve: 27 Meter --> 27 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

n = (ln(l_n/l₀))/(ln(4/3)) --> (ln(64/27))/(ln(4/3))

Evaluating ... ...

n = 3

STEP 3: Convert Result to Output's Unit

3 --> No Conversion Required

FINAL ANSWER

3 <-- Number of Iterations of Koch Curve

(Calculation completed in 00.004 seconds)

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Created by Jaseem K

IIT Madras (IIT Madras), Chennai

Jaseem K has created this Calculator and 100+ more calculators!

Verified by Nikita Kumari

The National Institute of Engineering (NIE), Mysuru

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< 5 Koch Curve Calculators

Number of Iterations of Koch Curve given Length after n Iterations

Go Number of Iterations of Koch Curve = (ln(Length of Koch Curve after n Iterations/Initial Length of Koch Curve))/(ln(4/3))

Initial Line Length of Koch Curve given Length after n Iterations

Go Initial Length of Koch Curve = (3/4)^Number of Iterations of Koch Curve*Length of Koch Curve after n Iterations

Length of Koch Curve after n Iterations

Go Length of Koch Curve after n Iterations = (4/3)^Number of Iterations of Koch Curve*Initial Length of Koch Curve

Initial Line Length of Koch Curve given Height

Go Initial Length of Koch Curve = 2*sqrt(3)*Height of Koch Curve

Height of Koch Curve

Go Height of Koch Curve = sqrt(3)/6*Initial Length of Koch Curve

Number of Iterations of Koch Curve given Length after n Iterations Formula

Number of Iterations of Koch Curve = (ln(Length of Koch Curve after n Iterations/Initial Length of Koch Curve))/(ln(4/3))
n = (ln(l_n/l₀))/(ln(4/3))

What is a Koch Curve?

The Koch curve is built by dividing a line into three equal segments, putting an equilateral triangle above the middle segment and removing the bottom line of this. This is repeated with the four new lines, and so on, infinitely. This makes the Koch curve a fractal with the Hausdorff dimension ln(4)/ln(3)≈1,26186 and infinite length. The single steps are called iterations.

How to Calculate Number of Iterations of Koch Curve given Length after n Iterations?

Number of Iterations of Koch Curve given Length after n Iterations calculator uses Number of Iterations of Koch Curve = (ln(Length of Koch Curve after n Iterations/Initial Length of Koch Curve))/(ln(4/3)) to calculate the Number of Iterations of Koch Curve, The Number of Iterations of Koch Curve given Length after n Iterations formula is defined as the number of steps n of iteration process after which the desired Koch Curve gets, and calculated using the length of the Koch Curve after n iterations. Number of Iterations of Koch Curve is denoted by n symbol.

How to calculate Number of Iterations of Koch Curve given Length after n Iterations using this online calculator? To use this online calculator for Number of Iterations of Koch Curve given Length after n Iterations, enter Length of Koch Curve after n Iterations (l_n) & Initial Length of Koch Curve (l₀) and hit the calculate button. Here is how the Number of Iterations of Koch Curve given Length after n Iterations calculation can be explained with given input values -> 3 = (ln(64/27))/(ln(4/3)).

FAQ

What is Number of Iterations of Koch Curve given Length after n Iterations?

The Number of Iterations of Koch Curve given Length after n Iterations formula is defined as the number of steps n of iteration process after which the desired Koch Curve gets, and calculated using the length of the Koch Curve after n iterations and is represented as n = (ln(l_n/l₀))/(ln(4/3)) or Number of Iterations of Koch Curve = (ln(Length of Koch Curve after n Iterations/Initial Length of Koch Curve))/(ln(4/3)). The Length of Koch Curve after n Iterations is the length of Koch Curve after completing n number of iterations on the original or initial length & The Initial Length of Koch Curve is the length of the curve which undergoing iteration to form the Koch Curve of respective iteration order.

How to calculate Number of Iterations of Koch Curve given Length after n Iterations?

The Number of Iterations of Koch Curve given Length after n Iterations formula is defined as the number of steps n of iteration process after which the desired Koch Curve gets, and calculated using the length of the Koch Curve after n iterations is calculated using Number of Iterations of Koch Curve = (ln(Length of Koch Curve after n Iterations/Initial Length of Koch Curve))/(ln(4/3)). To calculate Number of Iterations of Koch Curve given Length after n Iterations, you need Length of Koch Curve after n Iterations (l_n) & Initial Length of Koch Curve (l₀). With our tool, you need to enter the respective value for Length of Koch Curve after n Iterations & Initial Length of Koch Curve and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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