What is the formula for finding the area of a Koch snowflake?

Area of the Koch Snowflake

Area after first iteration: (using a = s/3)
Area after second iteration: (using a = s/32)
Area after third iteration: (using a = s/33)

How do you solve Koch snowflakes?

Problem

divide the line segment into three segments of equal length.
draw an equilateral triangle that has the middle segment from step 1 as its base and points outward.
remove the line segment that is the base of the triangle from step 2.

How many sides does a Koch snowflake have?

When we first start out, there are 3 sides to the triangle, each of length one unit. On the next iteration, there are 12 sides, each of length 1/3 unit (Each of the three straight sides of triangle is replaced with four new segments).

What is a infinite shape?

In geometry, an apeirogon (from the Greek words “ἄπειρος” apeiros: “infinite, boundless”, and “γωνία” gonia: “angle”) or infinite polygon is a generalized polygon with a countably infinite number of sides. Apeirogons are the two-dimensional case of infinite polytopes.

Is a snowflake infinite?

The areas enclosed by the successive stages in the construction of the snowflake converge to 85 times the area of the original triangle, while the perimeters of the successive stages increase without bound. Consequently, the snowflake encloses a finite area, but has an infinite perimeter.

Who discovered Koch snowflake?

Niels Fabian Helge von Koch
The Koch Snowflake was created by the Swedish mathematician Niels Fabian Helge von Koch.

How to calculate the number of sides of the Koch snowflake?

The Koch curve is continuous everywhere but differentiable nowhere. After each iteration, the number of sides of the Koch snowflake increase by a factor of 4, so the number of sides after n iterations is given by: N n = N n − 1 ⋅ 4 = 3 ⋅ 4 n. {\\displaystyle N_ {n}=N_ {n-1}\\cdot 4=3\\cdot 4^ {n}\\,.}

How is the Koch curve different from the fractal curve?

Variants of the Koch curve. The progression for the area converges to 2 while the progression for the perimeter diverges to infinity, so as in the case of the Koch snowflake, we have a finite area bounded by an infinite fractal curve. The resulting area fills a square with the same center as the original, but twice the area,…

How many times the area of a snowflake converges?

The progression for the area of the snowflake converges to 85 times the area of the original triangle, while the progression for the snowflake’s perimeter diverges to infinity. Consequently, the snowflake has a finite area bounded by an infinitely long line.

What do you do with a Koch snowflake?

The Koch snowflake is also known as the Koch island. The Koch snowflake along with six copies scaled by 1/√3 1 / 3 and rotated by 30° can be used to tile the plane [ Example ].

What is the formula for finding the area of a Koch snowflake? Area of the Koch Snowflake Area after first iteration: (using a = s/3) Area after second iteration: (using a = s/32) Area after third iteration: (using a = s/33) How do you solve Koch snowflakes? Problem divide the line segment into three segments…