# Sierpinski triangle

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The Sierpinski Triangle Deep within the realm of fractal math lies a fascinating triangle filled with unique properties and intriguing patterns. This is the Sierpinski Triangle, a fractal of triangles with an area of zero and an infinitely long perimeter. There are many ways to create this triangle and many areas of study in which it appears. Named after the Polish mathematician, Waclaw Sierpinski, the Sierpinski Triangle has been the topic of much study since Sierpinski first discovered it in

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[R] It will be quite difficult for us if we directly jump onto the subject because it is a pure mathematics .But I assure you that the base trick is simple and once you get it in your mind, whole concept with its mathematical beauty will be yours .So, it would be quite logical if we go with the fundamentals .Okay? Let me tell you first about “Fractal”, A fractal is a natural phenomenon (make a note of that because it appears that by creating fractals in nature such

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Subject Topic Create a written narrative of the evolution of the topic. Include significant contributions from cultures and individuals. Describe important current applications of the topic that would be of particular interest for students. Number Systems Complex Numbers The earliest reference to complex numbers is from Hero of Alexandria’s work Stereometrica in the 1st century AD, where he contemplates the volume of a frustum of a pyramid. The proper study first came about in the 16th century

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Aim, objective and Hypothesis The current study set out to explore the generalisability of counting behaviour and the understanding of the cardinal principle in blind children. To date, research in this area has focused mainly on typically developing children. Some researchers have undertaken studies in the atypical population; however, this is limited to disorders such as Down syndrome (Caycho, Gunn & Siegal, 1991), mental retardation (Baroody, 1986) and severe learning difficulties (Porter, 1998)

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What Students Should Know According to the learning progressions report, coming into third grade, students know how to analyze, compare, and classify two-dimensional shapes by their properties. When students do this, they relate and combine these classifications that they have made (The Common Core Standards Writing Team, p. 13). Because the students have built a firm foundation of several shape categories, these categories can be the “raw material” for thinking about the relationships between classes

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Friedrich Wilhelm August Froebel lived from April 21, 1782 to June 21, 1852. He was a German teacher, and he laid out the foundation for modern education. His observations and actions were based on the recognition that all children have different needs and capabilities, which at the time was a milestone in education. Furthermore, he invented the concept of "kindergarten," and he also created the educational toys that are known as Froebel Gifts. Froebel is from Oberweissbach, Schwarzburg-Rudolstadt

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\noindent $EH = HG = GF = FE$\hfill ---\ since $EFGH$ is a rhombus.\\ $AB = BC = DC = DA$\hfill ---\ since $ABCD$ is a square.\\ $BF = DH$\hfill since $AD = BG$ and $EF = GH$ and $EH = GF$.\\ Similarly, $AE = GC$ and $AH = BE = FC = DG$.\\ The four triangles $(AEH;\ EBF;\ FCG;\ DHG)$ are congruent by $SSS$.\\ Each angle in the corner of $ABCD$ is $90^{\circ}$\hfill ---\ since $ABCD$ is a square.\\ $A\hat{E}H + E\hat{H}A = 90^{\circ}$\hfill ---\ since $E\hat{A}H = 90^{\circ}$.\\ Similarly \$B\hat{E}F

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four integers - one, two, three, and four [1 + 2 + 3 + 4 = 10]. When written in dot notation these numbers formed a perfect triangle. Taken directly from Thomas Heath who was a civil servant and also one of the leading world experts on the history of mathematics is a list of theorems attributed to Pythagoras and his followers: (i) The sum of the angles of a triangle is equal to two right angles. Also the Pythagoreans knew the generalization, which states that a polygon with n sides has sum

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math the students were learning about polygons and their characteristics. Triangles have a first and last name describing the sides and types of angles. There are different types of quadrilaterals and other polygons with five for more signs. For the summative assessment given to the students by the cooperative teacher, the students had to identify the shapes by their name, number of sides, number of angles, and (for triangles) their “first and last names.” My lesson was titled “review stations”

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Background: In 1904, Helge von Koch identified a fractal that appeared to model the snowflake. The fractal was built by starting with an equilateral triangle and removing the inner third of each side, building another equilateral triangle where the side was removed, and then repeating the process indefinitely. The process is pictured below, showing the original triangle at stage zero, and the resulting figures after one, two and three iterations. Method: Let Nn=the number of sides, Ln=the length of

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