The Koch Snowflake
The snowflake model was created in 1904 by Helen von Koch. This snowflake appeared to be one of the earliest fractal curves. The fractal is built by starting with an equilateral triangle. One must remove the inner third of each side and replace it with another equilateral triangle. The process is repeated indefinitely. The length of each side is one which will help you determine the perimeter of each triangle. With having the perimeter of each triangle, the height can be determined so the area can be defined. The height must be determined because to use the formula A=12bh to find the area of the traingle, the height must be known. After repeating the process for the triangles, the graph below displays the number of sides (Nn) for each snowflake, the length of a single side (In), the length of the perimeter (Pn) and the area (An). In 0 1 2 3 1 1/3 1/9 1/27 Nn 3 12 48 192 Pn 3 4 16/3 64/9 An 3/4 3/4(1+13) 3/4(1+13+427) 3/4(1+13+427+16243)

The behavior of the graph above proves that each time a new snowflake is formed, the perimeter increases by 49. So, by simply multiplying 49to the area prior to, you will generate the area for the next sequence. When A4 occurs, these are the following results;

In 4 181

Nn 192

Pn 25627

An 3/4(1+13+427+16243+642187)

When A6 occurs, these are the following results; In 6 1729 Nn 3072 Pn 1024243 ) An 3/4(1+13+427+16243+642187+1024177147

The pattern that is emerged after experimenthing further into the snowflakes is An+1=An+(3*4n9n)A0 and n1. Theoretically the area gets too small to see so it is a limit is when N gets to 7. So, N could never reach with the area being noticable.

...Adrian Zwierzchowski
2 IB
Investigation – Von Koch’s snowflake curve
In this investigation I am going to consider a limit curve named after the Swedish mathematician Niels Fabian Helge von Koch. I will try to investigate the perimeter and area of Von Koch’s curve.
[pic]
The Koch’s curve has an infinite length because each time the steps above are performed on each line segment of the figure there are four times as many line segments, the length of each...

...the way our brains are wired?
Fractals are objects with infinite lengths that occupy finite volumes, resulting in a "fractional dimension" that is not 1-, 2-, or 3-D, but a combination of all three, depending on its spatial configuration.
The Kochsnowflake is the repetitive procedure of dividing the image into three equal parts and replacing the middle piece with two similar pieces.
Hypothesis
Fractals mimic nature. (true or false)
This is the basic belief of...

...Mathematical Investigation:
VON KOCH’S SNOWFLAKE CURVE
Ha Yeon Lee 11B
Mathematics HL
• Introduction:
➢ History of Von Koch’s Snowflake Curve
The Kochsnowflake is a mathematical curve, which is believed to be one of the earliest fractal curves with description. In 1904, a Swedish mathematician, Helge von Koch introduced the construction of the Koch curve on his...

...This piece of literature first appeared in the New Republic. It was written by former New York City mayor, Edward Koch. This essay was written primarily to justify his position in favor of capital punishment. He explains to readers that although there have been attacks on his opinion, he has closely examined the opposing arguments and still supports the death penalty. Edward Koch does an excellent job in his efforts to persuade those who are morally opposed to...

...A Report on Snowflakes Dessert Café, SS15, Subang Jaya
INTRODUCTION :
You might be wondering what is it about Snowflakes that makes a lot of people would line up just to enjoy a bowl of shaved ice. Well, it’s not just an ordinary bowl of dessert. Jimmy Tsai, owner of Snowflakes Dessert Café, came up with the idea of this business because he missed the Taiwanese desserts that his mother and grandmother used to make back in his hometown, Taichung...

...1843.
* Koch decided to change his area of study to medicine from natural science, as he aspired to be a physician.
* In July of 1867, following his graduation from medical school, Koch married Emma Adolfine Josephine Fraatz, and the two had a daughter, Gertrude, in 1868
* After his graduation in 1866, he worked as a surgeon in, and following his service, worked as a physician in what today is known as Wolsztyn, Poland the Franco-Prussian War
* He...

... ¬¬¬¬¬
ENGINEERING STABLE PROT¬¬¬EINS
Stable and soluble HIV spike proteins
Appendix
Abstract……………………………….................................................1
Introduction………………………………..........................................1
Structure and function of gp120 and gp41.…………………………2
Mutation 1……………………………….............................................5...

...physicist travels back in time to kill the apostle Paul." (This is the summary for my first novel, Transgression.) The sentence will serve you forever as a ten-second selling tool. This is the big picture, the analog of that big starting triangle in the snowflake picture.
When you later write your book proposal, this sentence should appear very early in the proposal. It's the hook that will sell your book to your editor, to your committee, to the sales force, to bookstore...