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Initial Line Length of Koch Curve given Height Calculator

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✖The Height of Koch Curve is the maximum vertical distance from base to the Koch Curve.ⓘ Height of Koch Curve [h]

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✖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 Height [l₀]

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Initial Line Length of Koch Curve given Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

Initial Length of Koch Curve = 2*sqrt(3)*Height of Koch Curve
l₀ = 2*sqrt(3)*h
This formula uses 1 Functions, 2 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

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.
Height of Koch Curve - (Measured in Meter) - The Height of Koch Curve is the maximum vertical distance from base to the Koch Curve.

STEP 1: Convert Input(s) to Base Unit

Height of Koch Curve: 8 Meter --> 8 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l₀ = 2*sqrt(3)*h --> 2*sqrt(3)*8

Evaluating ... ...

l₀ = 27.712812921102

STEP 3: Convert Result to Output's Unit

27.712812921102 Meter --> No Conversion Required

FINAL ANSWER

27.712812921102 ≈ 27.71281 Meter <-- Initial Length 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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< 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 Height Formula

LaTeX Go

Initial Length of Koch Curve = 2*sqrt(3)*Height of Koch Curve
l₀ = 2*sqrt(3)*h

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 Height?

Initial Line Length of Koch Curve given Height calculator uses Initial Length of Koch Curve = 2*sqrt(3)*Height of Koch Curve to calculate the Initial Length of Koch Curve, The Initial Line Length of Koch Curve given Height formula is defined as the actual length of the Koch Curve before all the iterations or the length of the line from which we start iterations to form the Koch Curve. Initial Length of Koch Curve is denoted by l₀ symbol.

How to calculate Initial Line Length of Koch Curve given Height using this online calculator? To use this online calculator for Initial Line Length of Koch Curve given Height, enter Height of Koch Curve (h) and hit the calculate button. Here is how the Initial Line Length of Koch Curve given Height calculation can be explained with given input values -> 27.71281 = 2*sqrt(3)*8.

FAQ

What is Initial Line Length of Koch Curve given Height?

The Initial Line Length of Koch Curve given Height formula is defined as the actual length of the Koch Curve before all the iterations or the length of the line from which we start iterations to form the Koch Curve and is represented as l₀ = 2*sqrt(3)*h or Initial Length of Koch Curve = 2*sqrt(3)*Height of Koch Curve. The Height of Koch Curve is the maximum vertical distance from base to the Koch Curve.

How to calculate Initial Line Length of Koch Curve given Height?

The Initial Line Length of Koch Curve given Height formula is defined as the actual length of the Koch Curve before all the iterations or the length of the line from which we start iterations to form the Koch Curve is calculated using Initial Length of Koch Curve = 2*sqrt(3)*Height of Koch Curve. To calculate Initial Line Length of Koch Curve given Height, you need Height of Koch Curve (h). With our tool, you need to enter the respective value for Height of Koch Curve 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 Height of Koch Curve. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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