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Mathematics: Its Historical Aspects, Wonders And Beyond [Mīkstie vāki]

(City Univ Of New York, Usa), (City University Of New York, Usa)
  • Formāts: Paperback / softback, 404 pages
  • Sērija : Problem Solving in Mathematics and Beyond 27
  • Izdošanas datums: 20-Jul-2022
  • Izdevniecība: World Scientific Publishing Co Pte Ltd
  • ISBN-10: 9811249334
  • ISBN-13: 9789811249334
Citas grāmatas par šo tēmu:
  • Mīkstie vāki
  • Cena: 61,22 €
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  • Formāts: Paperback / softback, 404 pages
  • Sērija : Problem Solving in Mathematics and Beyond 27
  • Izdošanas datums: 20-Jul-2022
  • Izdevniecība: World Scientific Publishing Co Pte Ltd
  • ISBN-10: 9811249334
  • ISBN-13: 9789811249334
Citas grāmatas par šo tēmu:

Whenever the topic of mathematics is mentioned, people tend to indicate their weakness in the subject as a result of not having enjoyed its instruction during their school experience. Many students unfortunately do not have very positive experiences when learning mathematics, which can result from teachers who have a tendency ""to teach to the test"". This is truly unfortunate for several reasons. First, basic algebra and geometry, which are taken by almost all students, are not difficult subjects, and all students should be able to master them with the proper motivational instruction. Second, we live in a technical age, and being comfortable with basic mathematics can certainly help you deal with life's daily challenges. Other, less tangible reasons, are the pleasure one can experience from understanding the many intricacies of mathematics and its relation to the real world, experiencing the satisfaction of solving a mathematical problem, and discovering the intrinsic beauty and historical development of many mathematical expressions and relationships. These are some of the experiences that this book is designed to deliver to the reader. The book offers 101 mathematical gems, some of which may require a modicum of high school mathematics and others, just a desire to carefully apply oneself to the ideas. Many folks have spent years encountering mathematical terms, symbols, relationships and other esoteric expressions. Their origins and their meanings may never have been revealed, such as the symbols +, -, =, p. ?, v, ?, and many others. This book provides a delightful insight into the origin of mathematical symbols and popular theorems such as the Pythagorean Theorem and the Fibonacci Sequence, common mathematical mistakes and curiosities, intriguing number relationships, and some of the different mathematical procedures in various countries. The book uses a historical and cultural approach to the topics, which enhances the subject matter and greatly adds to its appeal. The mathematical material can, therefore, be more fully appreciated and understood by anyone who has a curiosity and interest in mathematics, especially if in their past experience they were expected to simply accept ideas and concepts without a clear understanding of their origins and meaning. It is hoped that this will cast a new and positive picture of mathematics and provide a more favorable impression of this most important subject and be a different experience than what many may have previously encountered. It is also our wish that some of the fascination and beauty of mathematics shines through in these presentations.

About the Authors v
Introduction xvii
Chapter 1 All About Numbers and Symbols
1(1)
Unit 1 Some Ancient Number Systems
1(6)
Unit 2 The Origin of Our Numerals
7(2)
Unit 3 The History of Zero
9(3)
Unit 4 The Origin of the Equal Sign
12(2)
Unit 5 The Birth of Multiplication and its Symbol
14(4)
Unit 6 The Origin of the Division Symbols
18(3)
Unit 7 The Origins of Fractions
21(2)
Unit 8 The Emergence of Exponent Notation
23(2)
Unit 9 The Origin of the Square-Root Symbol
25(2)
Unit 10 The Origin of Percent %, Number #, and Dollar $ Symbols
27(3)
Unit 11 The Ubiquitous Number π
30(4)
Unit 12 One of the Earliest Approximations of it
34(2)
Unit 13 The Origin of the Basic Trigonometric Names: Sine, Tangent, and Secant
36(2)
Unit 14 How Numbers are Categorized
38(2)
Unit 15 Imaginary Numbers are Not Really Imaginary
40(7)
Unit 16 The Birth of Algebra
47(1)
Unit 17 The Infinity Concept and Its Symbol ∞
48(8)
Unit 18 The "Quad" in Quadratic
56(1)
Unit 19 Prime Numbers: Background and Properties
57(6)
Unit 20 Perfect Numbers
63(4)
Unit 21 Triangular Numbers and Their Relation to Square Numbers
67(4)
Unit 22 Numerology
71(3)
Unit 23 Very Small and Very Large Numbers
74(3)
Unit 24 The Googol is Much Older Than Google
77(2)
Unit 25 Armstrong or Narcissistic Numbers
79(4)
Unit 26 Friendly Numbers or Amicable Numbers
83(4)
Unit 27 Happy and Unhappy Numbers
87(3)
Unit 28 Repunits, Numbers Consisting Only of 1's
90(5)
Unit 29 Palindromic Numbers
95(6)
Unit 30 The Ubiquitous Number 1089
101(2)
Unit 31 Kaprekar Numbers
103(4)
Unit 32 The Transcendency of Transcendental Numbers
107(2)
Chapter 2 Arithmetic Curiosities
109(52)
Unit 33 How the Romans did Multiplication
109(4)
Unit 34 How Complex Calculations Were Done Before Electronics
113(7)
Unit 35 American and European Subtraction Algorithms
120(2)
Unit 36 Extracting a Square Root
122(1)
Unit 37 Divisibility by Prime Numbers
123(6)
Unit 38 Successive Percentages
129(2)
Unit 39 Casting Out Nines
131(4)
Unit 40 Division by Zero
135(1)
Unit 41 Mistaken Assumptions
136(3)
Unit 42 The Ulam-Collatz Loop
139(2)
Unit 43 A Cyclic Number Loop
141(3)
Unit 44 Curious Number Properties
144(10)
Unit 45 Magic Squares
154(7)
Chapter 3 Aspects of Measurement
161(34)
Unit 46 The Origin of Measurement
161(3)
Unit 47 The Metric System Versus the U.S. Customary System
164(4)
Unit 48 The Origins of Today's Calendar
168(5)
Unit 49 How Eratosthenes Measured the Earth
173(2)
Unit 50 The Origin of the Cartesian Plane
175(5)
Unit 51 Why the Normal Bell-Shaped Curve is Called Normal
180(3)
Unit 52 Measures of Central Tendency
183(3)
Unit 53 Comparing Means Algebraically
186(2)
Unit 54 Comparing the Three Means Geometrically
188(3)
Unit 55 The Rule of 72
191(4)
Chapter 4 Geometric Novelties
195(90)
Unit 56 The Platonic Solids
195(2)
Unit 57 Euler's Theorem Revisited
197(4)
Unit 58 The Beginnings of Geometry
201(5)
Unit 59 The Origin of the American Secondary School Geometry Course
206(3)
Unit 60 The Pythagorean Theorem and Its Origins
209(11)
Unit 61 President James A. Garfield's Contribution to Mathematics
220(3)
Unit 62 The Golden Ratio -- and the Golden Rectangle and Triangle
223(6)
Unit 63 The Center of Gravity of Triangles and Quadrilaterals
229(3)
Unit 64 Napoleon's Geometry Theorem
232(6)
Unit 65 Simson's Line
238(1)
Unit 66 The Nine-Point Circle
239(5)
Unit 67 A Famous Problem of Antiquity -- Angle Trisection
244(4)
Unit 68 The Ever-Present Equilateral Triangle
248(4)
Unit 69 The Four-Color Map Problem
252(3)
Unit 70 Optical Illusions
255(4)
Unit 71 The World of Non-Euclidean Geometries
259(5)
Unit 72 Introduction to Spherical Geometry
264(11)
Unit 73 Cartography is Mathematically Challenging
275(3)
Unit 74 A Look at Fractals
278(7)
Chapter 5 Probability
285(24)
Unit 75 The History of Probability
285(2)
Unit 76 The Famous Birthday Problem
287(2)
Unit 77 The Remarkable Probability in the Game of Craps
289(4)
Unit 78 Some Statements are Neither True nor False
293(2)
Unit 79 The Pigeonhole Principle
295(1)
Unit 80 The Heads and Tails Conundrum
296(1)
Unit 81 The Monty Hall Problem
297(3)
Unit 82 The False Positive Paradox
300(3)
Unit 83 Fair Division
303(6)
Chapter 6 A Potpourri of Mathematical Topics
309(66)
Unit 84 Logical Thinking
309(1)
Unit 85 More Mathematical Conundrums
310(2)
Unit 86 Mistakes in Mathematics
312(9)
Unit 87 The Hands of an Analog Clock
321(3)
Unit 88 Pythagorean Triples
324(3)
Unit 89 Fermat's Last Theorem
327(3)
Unit 90 Pure Mathematics and Prime Numbers
330(3)
Unit 91 The Fibonacci Numbers
333(7)
Unit 92 Diophantine Equations
340(3)
Unit 93 The Goldbach Conjecture
343(2)
Unit 94 Triskaidekaphobia
345(5)
Unit 95 The Parabola -- A Very Special Curve
350(5)
Unit 96 Kepler's Three Famous Laws
355(3)
Unit 97 Beyond the Quadratic Equation
358(3)
Unit 98 Evariste Galois -- A Short Brilliant Life
361(3)
Unit 99 A Look at Einstein's Special Relativity
364(2)
Unit 100 A Clear Look at Calculus
366(4)
Unit 101 Euler's Remarkable Relationship
370(5)
Index 375