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Initial Line Length of Koch Curve given Length after n Iterations Calculator

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✖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 [n]			+10% -10%
✖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 Line Length of Koch Curve given Length after n Iterations [l₀]

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Initial Line Length of Koch Curve given Length after n Iterations Solution

STEP 0: Pre-Calculation Summary

Formula Used

Initial Length of Koch Curve = (3/4)^Number of Iterations of Koch Curve*Length of Koch Curve after n Iterations
l₀ = (3/4)^n*l_n
This formula uses 3 Variables

Variables Used

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.
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.

STEP 1: Convert Input(s) to Base Unit

Number of Iterations of Koch Curve: 3 --> No Conversion Required
Length of Koch Curve after n Iterations: 64 Meter --> 64 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l₀ = (3/4)^n*l_n --> (3/4)^3*64

Evaluating ... ...

l₀ = 27

STEP 3: Convert Result to Output's Unit

27 Meter --> No Conversion Required

FINAL ANSWER

27 Meter <-- Initial Length of Koch Curve

(Calculation completed in 00.020 seconds)

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Created by Jaseem K

IIT Madras (IIT Madras), Chennai

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< Koch Curve Calculators

Initial Line Length of Koch Curve given Length after n Iterations

LaTeX 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

LaTeX 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

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

Height of Koch Curve

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

Initial Line Length of Koch Curve given Length after n Iterations Formula

LaTeX Go

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

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 Initial Line Length of Koch Curve given Length after n Iterations?

Initial Line Length of Koch Curve given Length after n Iterations calculator uses Initial Length of Koch Curve = (3/4)^Number of Iterations of Koch Curve*Length of Koch Curve after n Iterations to calculate the Initial Length of Koch Curve, The Initial Line Length of Koch Curve given Length after n Iterations formula is defined as the length of line from which Koch Curve forms after iterations, and calculated using the length after n iterations. Initial Length of Koch Curve is denoted by l₀ symbol.

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

FAQ

What is Initial Line Length of Koch Curve given Length after n Iterations?

The Initial Line Length of Koch Curve given Length after n Iterations formula is defined as the length of line from which Koch Curve forms after iterations, and calculated using the length after n iterations and is represented as l₀ = (3/4)^n*l_n or Initial Length of Koch Curve = (3/4)^Number of Iterations of Koch Curve*Length of Koch Curve after n Iterations. The Number of Iterations of Koch Curve is the number of steps completed during the process of iteration in the formation of Koch Curve & 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.

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

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

How many ways are there to calculate Initial Length of Koch Curve?

In this formula, Initial Length of Koch Curve uses Number of Iterations of Koch Curve & Length of Koch Curve after n Iterations. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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