Mathematics and the Arts Kokichi Sugihara 1. Fractal Voronoi Diagrams The Voronoi diagram represents the partition of the plane into territories‚ where each territory consists of points nearest to the associated generators. Starting with a small number of generators‚ we add generators at random‚ simulate territory competing‚ and assign colors to the resulting diagram. Then‚ we get something like artistic patterns. Search for the point with the maximum F (θ ‚ ϕ ) in the (θ ‚ ϕ ) space. 3. Generation
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1 Engineering Mathematics 1 (AQB10102) CHAPTER 1: NUMBERS AND ARITHMETIC 1.1 TYPE OF NUMBERS NEGATIVE INTEGER - POSITIVE AND REAL NUMBERS (R) • • Numbers that can be expressed as decimals Real Number System: • Consist of positive and negative natural numbers including 0 Example: …‚ -5‚ -4‚ -3‚ -2‚ -1‚ 0‚ 1‚ 2‚ 3‚ 4‚ 5‚ … • All numbers including natural numbers‚ whole numbers‚ integers‚ rational numbers and irrational numbers are real numbers Example: 4 = 4
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mother of Europe’s languages. India was the mother of our philosophy‚ of much of our mathematics‚ of the ideals embodied in Christianity... of self-government and democracy. In many ways‚ Mother India is the mother of us all." - Will Durant‚ American Historian 1885-1981 Mathematics is an important field of study. Mathematics is essential as it helps in developing lots of realistic skills‚ in fact study of mathematics itself include the concepts related to the routine lives of human. It not only develops
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2012 Experiment 32: Identification of a Conjugated Diene from Eucalyptus oil Introduction In this experiment‚ the purpose was to prepare the Diels-Alder adduct of the unknown conjugated diene in Eucalyptus oil and determine the approximate percentage of diene in Eucalyptus oil. To discover the product of this reaction‚ isolate the adduct‚ and classify the diene from the melting point of its adduct. The unknown was one of four conjugated dienes. Maleic anhydride
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Randse Afrikaanse Universiteit Rand Afrikaans University TOEGEPASTE WISKUNDE 1B APPLIED MATHEMATICS 1B 1. P.4.3.1 2. P.4.3.2 3. P.4.3.3 Vraag 4 Vir die massa in P.4.3.3 by t = 3sek. bereken: (a) Die hoekspoed van die massa om die oorsprong. (b) Die krommingstraal van die boom. (c) Die koordinate van die krommingsmiddelpunt. Question 4 For the mass in P.4.3.3 at t = 3sec. calculate: (a) The angular velocity of the mass around the origin. (b) The radius of curvature of the trajectory. (c) The coordinates
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Rhodes University Mathematics Education Project‚ South Africa R.Spanneberg@ru.ac.za This paper is a report of a study into the impact of a professional development programme designed to bring about changes in the classroom practices of teachers and change in their beliefs and attitudes. The programme is offered to in-service teachers of mathematics over a period of two years. The study is focussed on the assumption that what a teacher believes about mathematics and teaching mathematics is integrally
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in jump-starting cognitive development‚ which is the development of thinking‚ problem solving‚ and memory. There was a time that people believed young children and adults had alike thought processes. However‚ Swiss-born clinical psychologist‚ Jean Piaget reversed this notion by theorizing that there are four separate stages to this process that occur from the time before your first birthday up until you begin approaching adulthood. The four stages are the sensorimotor‚ preoperational‚ concrete operations
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Mathematics in Gaming: Understanding can help you win! Prafull S Chapate1 Vimaltai Tidke Convent‚ Narendranagar Nagpur-440027‚ Maharashtra‚ India Abstract In this paper‚ we present you detail relationship between mathematics and some of the games you encountered in your daily life. Mathematical knowledge of these games gives you an edge over your mathematically ignorant opponent and who knows may help you win the game and money. 1. Introduction For entertainment many people play
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of any circle’s circumference to its diameter in the Euclidean plane; this is the same value as the ratio of a circle’s area to the square of its radius. It is approximately equal to 3.14159265 in the usual decimal notation. Many formulae from mathematics‚ science‚ and engineering involve π‚ which makes it one of the most important mathematical constants. π is an irrational number‚ which means that its value cannot be expressed exactly as a fraction m/n‚ where m and n are integers. Consequently
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ADDITIONAL MATHEMATICS PROJECT YEAR 2011 FORM5 NAME : ONG KAH HONG FORM : 5 CEMERLANG NO I/C : 940422-06-5075 TITLE :Crude Oil TEACHER : MISS PHUA CHUI CHUI CONTENTS 1. Introduction Introduction of project……………. Introduction of integration………... Definition of integration………….. History of integration…………….. 2. Problem Solving Part1………………………………. Part2………………………………. Part3………………………………. Part4………………………………. Part5………………………………
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