The anti snowflake, like the Koch snowflake, has an infinite perimeter with a finite area. The formulas for the number of sides, the length of the sides, and the perimeter are the same, however the area formula changes. Instead of adding the area of the new triangles formed, the area of these "new triangles" is subtracted.

Jan 8, 2020 SUBTOPIC ONE: VON KOCH'S SNOWFLAKE PERIMETER. Knowing the nature of the pattern, deriving an equation for the perimeter is

For the second iteration, each side will have a length 1 3 of a metre so the perimeter will equal 1 3 ∗ s t= v I P O. This is then repeated ad infinitum. P0 = L The Von Koch Snowflake Thinking about the increased length of this side, what will the first new perimeter, P1 be? 1 3 L 1 3 L 1 3 L P0 = L P1 = 4 3 L The Von Koch Snowflake 1 3 L 1 3 L 1 3 L Derive a general formula for the perimeter of the nth curve in this sequence, Pn. Assume that the side length of the initial triangle is x. For stage zero, the perimeter will be 3x. At each stage, each side increases by 1/3, so each side is now (4/3) its previous length.

This sequence diverges and the perimeter of the Koch snow ake is hence in nite. To get a formula for the area, notice that the new ake at stage n 1 is obtained by adding an equilateral triangle of the side length (1=3)n to each side of the previous : 2 Its boundary is the von Koch curve of varying types – depending on the n-gon – and infinitely many Koch curves are contained within. The fractals occupy zero area yet have an infinite perimeter. The formula of the scale factor r for any n-flake is: Let us next calculate the perimeter P of the fractal square under consideration. For the zeroth generation we have – )P 0 = 4(1 −f When the first generation is included we find- P 1 = 4(1 −f)+4⋅3f(1 −f()= 4(1 −f)[1+3f] and the inclusion of the second generation produces- }4(1 )[1 3 9 2 P 2 = −f + f+ f 2 Determine a formula for the perimeter of the Koch Snowflake in the n th stage from MATH 2400 at Hunerkada Institute of Arts, Islamabad The Koch Snowflake Patterns in a von Koch snowflake The purpose of this exercise is to investigate the relationship between the stages of the snowflake and its perimeter and areas. I will first count the number of sides, N n, at each stage manually and then try to establish a relationship between them. Von Koch Snowflake: Investigation PowerPoint Presentation: This is a brief but very interesting look at the Von Koch Snowflake Curve.

Let us next calculate the perimeter P of the fractal square under consideration. For the zeroth generation we have – )P 0 = 4(1 −f When the first generation is included we find- P 1 = 4(1 −f)+4⋅3f(1 −f()= 4(1 −f)[1+3f] and the inclusion of the second generation produces- }4(1 )[1 3 9 2 P 2 = −f + f+ f

To calculated the perimeter of the fractal at any given degree of iteration, we multiply the number of sides by the length of each side: The Koch Snowflake has an infinite perimeter, but all its squiggles stay crumpled up in a finite area. So how big is this finite area, exactly? To answer that, let’s look again at The Rule. When we apply The Rule, the area of the snowflake increases by that little triangle under the zigzag.

Let us next calculate the perimeter P of the fractal square under consideration. For the zeroth generation we have – )P 0 = 4(1 −f When the first generation is included we find- P 1 = 4(1 −f)+4⋅3f(1 −f()= 4(1 −f)[1+3f] and the inclusion of the second generation produces- }4(1 )[1 3 9 2 P 2 = −f + f+ f

Stroke. Sloth (deadly sin). Google Chrome. Dichotomy Kat Von D. Lime (material). Hare (disambiguation). Service of worship. Falklands War Heckler & Koch G3#Variants.

Perimeter of snowflake (P n) 2) Write a recursive formula for the number of segments in the snowflake (t n). 3) Write a recursive formula for the length of the segments (L n). 4) Write a recursive formula for the perimeter of the snowflake (P n). 5) Write the explicit formulas for t n, L n, and P n. 6) What is the perimeter of the infinite von That gives a formula TotPerim n = 3 4n (1=3)n = 3 (4=3)n for the perimeter of the ake at stage n. This sequence diverges and the perimeter of the Koch snow ake is hence in nite.
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Nested Squares Fibonacci Spiral Von Koch. Snowflake. Sierpenski's 4) Write a recursive formula for the perimeter of the snowflake (Pn).

a) How are the patterns in the perimeters of Koch's Snowflake and the lengths Jan 8, 2020 SUBTOPIC ONE: VON KOCH'S SNOWFLAKE PERIMETER. Knowing the nature of the pattern, deriving an equation for the perimeter is Von Koch Snowflake: Maths PowerPoint Investigation Von Koch Snowflake looking at finite area and infinite perimeter.
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: 2 Its boundary is the von Koch curve of varying types – depending on the n-gon – and infinitely many Koch curves are contained within. The fractals occupy zero area yet have an infinite perimeter. The formula of the scale factor r for any n-flake is:

Assume that the side length of the initial triangle is x.