Buch, Englisch, 320 Seiten, Format (B × H): 155 mm x 234 mm, Gewicht: 462 g
A Historical and Mathematical Journey
Buch, Englisch, 320 Seiten, Format (B × H): 155 mm x 234 mm, Gewicht: 462 g
ISBN: 978-0-470-58718-8
Verlag: Wiley
Explores the development of the ellipse and presents mathematical concepts within a rich, historical context
The Ellipse features a unique, narrative approach when presenting the development of this mathematical fixture, revealing its parallels to mankind's advancement from the Counter-Reformation to the Enlightenment. Incorporating illuminating historical background and examples, the author brings together basic concepts from geometry, algebra, trigonometry, and calculus to uncover the ellipse as the shape of a planet's orbit around the sun.
The book begins with a discussion that tells the story of man's pursuit of the ellipse, from Aristarchus to Newton's successful unveiling nearly two millenniums later. The narrative draws insightful similarities between mathematical developments and the advancement of the Greeks, Romans, Medieval Europe, and Renaissance Europe. The author begins each chapter by setting the historical backdrop that is pertinent to the mathematical material that is discussed, equipping readers with the knowledge to fully grasp the presented examples and derive the ellipse as the planetary pathway. All topics are presented in both historical and mathematical contexts, and additional mathematical excursions are clearly marked so that readers have a guidepost for the materials' relevance to the development of the ellipse.
The Ellipse is an excellent book for courses on the history of mathematics at the undergraduate level. It is also a fascinating reference for mathematicians, engineers, or anyone with a general interest in historical mathematics.
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Weitere Infos & Material
PREFACE.
CHAPTER 1: INTRODUCTION.
CHAPTER 2: THE TRAIL: STARTING OUT.
2.1 A Sticky Matter.
2.2 Numbers.
2.2.1 Integers, Rational Numbers, and Irrational Numbers.
2.2.2 The Size of the Irrational Numbers.
2.2.3 Suitability of Rationals and the Decimal System.
2.2.4 Rational and Irrational Outcomes.
CHAPTER 3: THE SPACE: GEOMETRY.
3.1 Euclidean Space, Dimension and Rescaling.
3.1.1 Euclidean Space and Objects.
3.1.2 Euclidean Space in Higher Dimensions.
3.1.3 Unit Measurements and Measures of Objects.
3.1.4 Rescaling, Measurement, and Dimension.
3.1.5 Koch's Snowflake, a Fractal Object.
3.2 Measurements of Various Objects.
3.2.1 Pythagorean Theorem, Length of the Hypotenuse.
3.2.2 Cavalieri's Theorem in Two Dimensions.
3.2.3 Cavalieri's Theorem, Archimedes Weighs In.
3.2.4 Simple Applications of Cavalieri’s Theorem.
3.2.5 The Circle.
3.2.6 Surface Area of the Cone.
3.2.7 Cavalieri's Theorem a Stronger Version in Three Dimensions.
3.2.8 Generalized Pyramids.
3.2.9 The Sphere as a Generalized Pyramid.
3.2.10 The Surface Area and Volume of the Sphere.
3.2.11 Equal-Area Maps, Another Excursion.
CHAPTER 4: THE LANGUAGE: ALGEBRA.
4.1 Cartesian Coordinates and Translation of the Axes.
4.1.1 Intersections of Geometric Objects as Solutions to Equations.
4.1.2 Translation of Axis and Object.
4.2 Polynomials.
4.2.1 Lines.
4.2.2 Parabolas and the Quadratic Equation.
4.3 Circles.
4.3.1 Equations for a Circle.
4.3.2 Archimedes and the Value of p.
4.3.3 Tangent Lines to a Circle.
4.4 The Four-Dimensional Sphere.
4.4.1 Pythagorean Theorem in Higher Dimensions.
4.4.2 Measurements in Higher Dimensions and n-Dimensional Cubes.
4.4.3 Cavalieri's Theorem.
4.4.4 Pyramids.
4.4.5 The n<
