Height of Koch Curve Calculator

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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 Length of Koch Curve [l₀]

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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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Formula

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Height of Koch Curve

Formula

`"h" = sqrt(3)/6*"l"_{"0"}`

Example

`"7.794229m"=sqrt(3)/6*"27m"`

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Height of Koch Curve Solution

STEP 0: Pre-Calculation Summary

Formula Used

Height of Koch Curve = sqrt(3)/6*Initial Length of Koch Curve
h = sqrt(3)/6*l₀
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

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

Initial Length of Koch Curve: 27 Meter --> 27 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h = sqrt(3)/6*l₀ --> sqrt(3)/6*27

Evaluating ... ...

h = 7.79422863405995

STEP 3: Convert Result to Output's Unit

7.79422863405995 Meter --> No Conversion Required

FINAL ANSWER

7.79422863405995 ≈ 7.794229 Meter <-- Height of Koch Curve

(Calculation completed in 00.006 seconds)

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Credits

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

Nikita Kumari has verified this Calculator and 600+ more calculators!

< 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

Height of Koch Curve Formula

Height of Koch Curve = sqrt(3)/6*Initial Length of Koch Curve
h = sqrt(3)/6*l₀

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 Height of Koch Curve?

Height of Koch Curve calculator uses Height of Koch Curve = sqrt(3)/6*Initial Length of Koch Curve to calculate the Height of Koch Curve, The Height of Koch Curve formula is defined as the perpendicular distance from the bottom level to the highest point of the Koch Curve. Height of Koch Curve is denoted by h symbol.

How to calculate Height of Koch Curve using this online calculator? To use this online calculator for Height of Koch Curve, enter Initial Length of Koch Curve (l₀) and hit the calculate button. Here is how the Height of Koch Curve calculation can be explained with given input values -> 7.794229 = sqrt(3)/6*27.

FAQ

What is Height of Koch Curve?

The Height of Koch Curve formula is defined as the perpendicular distance from the bottom level to the highest point of the Koch Curve and is represented as h = sqrt(3)/6*l₀ or Height of Koch Curve = sqrt(3)/6*Initial Length of Koch Curve. 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 Height of Koch Curve?

The Height of Koch Curve formula is defined as the perpendicular distance from the bottom level to the highest point of the Koch Curve is calculated using Height of Koch Curve = sqrt(3)/6*Initial Length of Koch Curve. To calculate Height of Koch Curve, you need Initial Length of Koch Curve (l₀). With our tool, you need to enter the respective value for 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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