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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MATHEMATICS OF INVESTMENT Simple Interest If you borrow a car from a car rental company or if you live in someone else’s house or apartment‚ you have to pay rent. Like paying rent for the use of a car or a house‚ you also have to pay rent for the money you borrowed. This is called interest. People like Marco earn by charging interest on loans. Banks earn most of their income from the interest that people pay for the amounts they borrow. How much interest one has to pay depends on three factors:
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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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MATERIALS 9 GRADING SYSTEM 10 LEARNING COMPETENCIES 11 SAMPLE LESSON PLANS 30 INTRODUCTION This Handbook aims to provide the general public – parents‚ students‚ researchers‚ and other stakeholders – an overview of the Mathematics program at the secondary level. Those in education‚ however‚ may use it as a reference for implementing the 2002 secondary education curriculum‚ or as a source document to inform policy and guide practice. For quick reference‚ the Handbook is
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SOUTH AFRICAN MATHEMATICS OLYMPIAD Organised by the SOUTH AFRICAN MATHEMATICS FOUNDATION 2012 FIRST ROUND SENIOR SECTION: GRADES 10‚ 11 AND 12 19 March 2012 Time: 60 minutes Number of questions: 20 Instructions 1. This is a multiple choice question paper. Each question is followed by answers marked A‚ B‚ C‚ D and E. Only one of these is correct. 2. Scoring rules: 2.1. Each correct answer is worth 5 marks. 2.2. There is no penalty for an incorrect answer or any unanswered question. 3. You
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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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GENERAL AND SPECIFIC COMPETENCIES IN MATHEMATICS IV (Advanced Algebra‚ Trigonometry and Statistics) A. Functions 1. Demonstrate knowledge and skill related to functions in general 1.1 Define a function 1.2 Differentiate a function from a mere relation * real life relationships * set of ordered pairs * graph of a given set of ordered pairs * vertical line test * given equation 1.3 Illustrate the meaning of the functional notation f(x) 1.4 Determine the value of
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Zero is a number and a digit used in mathematics to represent that number in numerals. Zero is not a natural number but it is the smallest whole number. There are two important uses of zero. Firstly‚ in place value number system it is used as empty place indicator. Hence‚ in this number‚ 5102‚ the positions of 5 and one are correct just because of the inclusion of zero. Five is denoting a thousandth place value. Similarly if we omit zero from 5102 that is 512‚ then 5 denote a hundredth place value
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Zero in Mathematics Zero as a number is incredibly tricky to deal with. Though zero provides us with some useful mathematical tools‚ such as calculus‚ it presents some problems that if approached incorrectly‚ lead to a breakdown of mathematics as we know it. Adding‚ subtracting and multiplying by zero are straightforward. If c is a real number‚ c+0=c c-0=c c x 0=0 These facts are widely known and regarded to hold true in every situation. However‚ division by zero is a far more complicated
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[edit] Mathematics [edit] Pi as irrational Aryabhata worked on the approximation for Pi (π)‚ and may have come to the conclusion that π is irrational. In the second part of the Aryabhatiyam (gaṇitapāda 10)‚ he writes: caturadhikam śatamaṣṭaguṇam dvāṣaṣṭistathā sahasrāṇām ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ. "Add four to 100‚ multiply by eight‚ and then add 62‚000. By this rule the circumference of a circle with a diameter of 20‚000 can be approached."[12] This implies that the
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