Mathematical Investigation: VON KOCH’S SNOWFLAKE CURVE Ha Yeon Lee 11B Mathematics HL • Introduction: ➢ History of Von Koch’s Snowflake Curve The Koch snowflake 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 paper called, “On a continuous curve without tangents, constructible from elementary geometry”. ➢ In this mathematical task, I am going to investigate how the area and perimeter of a shape/curve changes and find out whether they increase by the same number every time,as the following process is repeated: …show more content…
⇒ The investigation of the area begins by supposing that C0, the initial curve (an equilateral triangle) has a total area of 1 unit2. [pic] The area of the initial curve is, therefore, [pic] [pic] [pic] = [pic] [pic] = 1 -First Iteration: *Since s2 = [pic], Area of C1 is [pic]units2. -Second Iteration: *Since s2 = [pic], Area of C2 is [pic]units2. -Third Iteration: *As s2 = [pic], Area of C3 is [pic]units2. Based on my findings in the area of the Koch curve, I created a table that will allow me to see general patterns much easily: |n (number of iterations) |Area (in unit2) | |0 |1 |1 | |1 |1+[pic]
The history of the united states is illustrated and told in A Patriot’s History of the United States written by Larry Schweikart and Michael Allen and A People’s History of the United States written by Howard Zinn. Both authors chronicles the history of the united states from the discovery of the new world to some of the more recent events, however with contrasting opinions and perspective . Larry Schweikart and Michael Allen curves towards a more conservative view with focus on a glorified america where sacrifice was necessary for the betterment and advancement of the people. On the other hand Howard Zinn focuses on views from the suffering or underprivileged groups that seems to show a pessimistic
Carl Jung thought that the form of a spiral represented the idea of “eternal return” in the pattern of human thought and insisted that the archetypal symbol represented the cosmic force (Bobroff, p. 27). Various ancient cultures viewed the spiral as a symbol for journey, growth, and evolution. From timeless edifices to contemporary architecture, one can observe the spiral form in building structures; such as staircases, domes, and spires. One doesn’t have to look very hard to see spirals in their everyday lives, take the golden ratio for example. The golden ratio can be expressed in the naturally occurring patterns in various plants and will also reflect the Fibonacci number sequence in the same manner. A pine cone is a perfect illustration of this, as are many succulents. Who knew that a simple image could represent so much, to so many, so differently.
The Eichmann trial reveals a lot about the strengths and limitations of the “the trial” to achieve justice in such cases. The reason of a trial is to render justice; even the ethical of underlying motives, as mentioned in the novel, “the making of a record of the Hitler regime which the withstand the test of history… Nuremburg Trials, can only detract the laws main business: to weigh the charges brought against the accused, to render judgement, and to mete out due punishment” (253). The judgement in the Eichmann case, whose first two sections had been written in respond to the better cause idea as it was changed into expanded both inside and outside the out room, could not have been clearer in this respect. As proven in the novel, it states
It is official; Richard "Bruno" Hauptmann has now been executed by an electric chair. The man hated all around the world is now gone for a crime that has been dubbed "crime of the century". I am just an average citizen of the USA and like many others, I was very curious and passionate about this case. On the night of March 1, 1932, Richard Hauptmann became infamous for the brutal kidnapping and killing of Charles Lindberg's 20-month-old son Charles Lindbergh Jr. How could he have done something so evil to the most loved family in America?
The mean area (A) can be calculated by using the following Equation 4, where d is average diameter of the measured dowel. The volume of the dowel is then calculated by multiplying the area by the length.
The area of a right triangle is 2. The length of the base is the same as the length of the height. Find this length.
areas, to have the equal results for all and for all to have the same
The lines would start by going up until it gets to 12 then would begin to bounce around from increase to decrease.
perimeter of big rectangles equals scale factor times perimeter of small rectangle equals scale factor times 58 & it results with 4.5.
9) Since you are plotting displacement on the y-axis and time on the x-axis, this is an example
Knowing this information, you need to first tell me, and then show this in your graph:
My infatuation in fractals began freshmen year at Greeley after taking a Seminar with one of the seniors. I’m not sure exactly when simple interest turned to a kind of obsession, but during that lesson something seemed to click. It seemed as if this was the universe’s answer to everything; the mystery was solved, however complex the answer was to understand. I’m still not sure if I was misunderstanding the lesson, or if I had somehow seen it for what it really was; a pattern to describe the way the universe works.
Surface area is a two-dimensional measurement, and is proportional to the square of its length.