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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By using Koch’s postulates‚ it was determined that Pseudomonas syringae was the bacteria causing rot. There are four criteria that must be met when using Koch’s postulates. They are that the organism must be fund in all infected‚ the organism must be isolated in pure culture then once reinnoculated in a healthy host‚ must cause the same symptoms and last‚ the organism must be reisolated in pure culture. All of Koch’s postulates were demonstrated with the tomato. Introduction: Koch’s postulates
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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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Koch’s Postulates Introduction Koch created four guidelines to determine the causal agents of disease in humans‚ animals‚ and plants. Koch proved that a disease-causing agent could be transferred from one organism to another and create the same illness. Isolation of pure cultures and the introduction of the disease-causing agent to a healthy organism will transmit the disease and infect the inoculated organism. Koch’s four guidelines by which one must follow to transmit a disease from an infected
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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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To what extent was Bismarck responsible for the unification of Germany in 1871 and account for the effect this had on the balance of power in Europe‚ any threats faced due to this imbalance and how Bismarck countered these threats. Otto von Bismarck‚ a charismatic diplomat and first chancellor of Germany‚ was one of the main driving forces behind the unification of the pre-German states. By opposing socialism and...... into the German Empire. His actions and results would usurp the balance of
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here’s how snowflakes are made‚ how they form‚ and how they stick to the ground. You may be shocked by how they form. Snowflakes are very unique in their own way. To start with‚ snowflakes form when cold water evaporates. When water reaches a certain level of the atmosphere and its 32 degrees Fahrenheit‚ or less‚ water vapor changes from gas to rock solid‚ that is‚ frozen water called ice crystals. Ice crystals form with dust and dirt in the air. These ice crystals are called snowflakes. Fluffy snow
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instruments used are tambourines‚ trombones‚ tuba‚ trumpet‚ and piccolos. The speed in “Waltz of the Snowflakes” is very fast and then it slows back down and speeds up again. The mood to me is a cheerful mood and loud. The volume is very upbeat and higher pitched. The composition is very complex and uses many instruments and pitches. What Comes to Mind? When I listen to “Waltz of the Snowflakes” I think of many things. The one thing that I mainly think of is the time when there were ball dances
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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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