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 being one-third the length of the
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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”
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The Koch Snowflake Math Mock Exploration Shaishir Divatia Math SL 1 The Koch Snowflake The Koch Snowflake is a fractal identified by Helge Von Koch‚ that looks similar to a snowflake. Here are the diagrams of the first four stages of the fractal - 1. At any stage (n) the values are denoted by the following – Nn - number of sides Ln - length of each side Pn - length of perimeter An - Area of snowflake Mentioned below are the values of these above variables‚ for the first 4 stages
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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
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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 Koch snowflake 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 fractals‚ and a common concept among
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Classic Koch Snowflake and a Variation of the Koch Snowflake Jarred Sareault Introduction: In this project‚ we need to find the area and perimeter of both the Classic and Variation Koch Snowflake for the first five levels. Also we need to create and implement general forms for the area and perimeter of the Classic/Variation Snowflakes to find the total area and perimeter of the final snowflake for each. For both the Classic and Variation Koch Snowflake‚ an equilateral triangle is used to start.
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THE S-CURVE Introduction The first time most project managers become aware of the existence of S Curves is when they are requested by the client or senior management to include one in their next progress report. The following explains what the mysterious S Curve is‚ why it is an important project management tool‚ and how to generate one. What is a S Curve? A S Curve is defined as "a display of cumulative costs‚ labour hours or other quantities plotted against time. The name derives from
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S-curve describes how the performance or cost characteristics of a technology change with time and continued investments. While the horizontal axis shows the history (time and investment) of technical innovations‚ the vertical axis shows some problems of product performance or cost competitiveness. The pace of improvement slows when the established technology is improved and approaching its maturity. Many problems which a new technology has to face with are solved over time and with investment
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Examine the salient features of the Phillips`s Curves. How might elementary textbooks be criticised for writing ‘inflation’ on the vertical axis? Introduction Philips curve‚ named after A.W. Philips‚ has caused many fierce debates in the area of macroeconomics since the World War II. Based on the data of wages and employment in UK from 1861to 1957‚ Phillips concluded that there had been an inverse relationship between the percentage rate of unemployment and the percentage rate of change in
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Assignment 2 Limitations of the S-Curve 1. Companies use the technology S-curve analysis as a tool in planning a technology strategy for the organization. It has been observed that technology develops in an S-curve pattern. In the beginning progress for any new technology is slow. As an expertise in the technology builds up‚ progress moves at a rapid pace. After a while‚ however‚ the technology matures and progress slows (Shane‚ 2009). S-curve analysis is not only used to plot the development
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