Mathematical Expeditions: Chronicles by the ExplorersSpringer Science & Business Media, 1. des. 2013 - 278 sider This book contains the stories of five mathematical journeys into new realms, told through the writings of the explorers themselves. Some were guided by mere curiosity and the thrill of adventure, while others had more practical motives. In each case the outcome was a vast expansion of the known mathematical world and the realization that still greater vistas remained to be explored. The authors tell these stories by guiding the reader through the very words of the mathematicians at the heart of these events, and thereby provide insight into the art of approaching mathematical problems. The book can be used in a variety of ways. The five chapters are completely independent, each with varying levels of mathematical sophistication. The book will be enticing to students, to instructors, and to the intellectually curious reader. By working through some of the original sources and supplemental exercises, which discuss and solve - or attempt to solve - a great problem, this book helps the reader discover the roots of modern problems, ideas, and concepts, even whole subjects. Students will also see the obstacles that earlier thinkers had to clear in order to make their respective contributions to five central themes in the evolution of mathematics. |
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Resultat 1-5 av 67
Side 4
... follows from Proposition 30 [ 51 , Vol . I , p . 316 ] , for which the parallel postulate is necessary ( Exercise 1.2 ) . The first source in this chapter is Proposition 32 from Book I of the Elements , which asserts that the angle sum ...
... follows from Proposition 30 [ 51 , Vol . I , p . 316 ] , for which the parallel postulate is necessary ( Exercise 1.2 ) . The first source in this chapter is Proposition 32 from Book I of the Elements , which asserts that the angle sum ...
Side 7
... follows that of Saccheri in its approach . Lambert introduces his treatise with : This work deals with the ... follow the teachings of others but look for a basis for their convictions and do not wish to give up the least bit of rigor ...
... follows that of Saccheri in its approach . Lambert introduces his treatise with : This work deals with the ... follow the teachings of others but look for a basis for their convictions and do not wish to give up the least bit of rigor ...
Side 10
... follows . But Laplace believed that this similarity is inherent in the physical laws of space . A particularly clear ... follow from the others . Geometry was inextricably tied to space , our physical universe . And space was considered ...
... follows . But Laplace believed that this similarity is inherent in the physical laws of space . A particularly clear ... follow from the others . Geometry was inextricably tied to space , our physical universe . And space was considered ...
Side 19
... follows a different approach [ 88 ] , instead taking words like point and line as undefined terms , about which one simply supposes basic properties that dictate how they interact with each other . For Euclid , these assumed ...
... follows a different approach [ 88 ] , instead taking words like point and line as undefined terms , about which one simply supposes basic properties that dictate how they interact with each other . For Euclid , these assumed ...
Side 22
... follow- ing [ 51 , Vol . I , p . 316 ] . Proposition 31 implies that there is only one straight line through A parallel to BC , but does not actually prove this . However , this fact will follow from Proposition 30 ( whose proof , which ...
... follow- ing [ 51 , Vol . I , p . 316 ] . Proposition 31 implies that there is only one straight line through A parallel to BC , but does not actually prove this . However , this fact will follow from Proposition 30 ( whose proof , which ...
Innhold
1 | |
Taming the Infinite | 54 |
3 | 69 |
Calculating Areas and Volumes | 89 |
1 | 95 |
4 | 123 |
5 | 129 |
7 | 150 |
Fermats Last Theorem | 156 |
The Search for an Elusive Formula | 204 |
References | 259 |
Credits | 269 |
Andre utgaver - Vis alle
Mathematical Expeditions: Chronicles by the Explorers Reinhard Laubenbacher,David Pengelley Begrenset visning - 2000 |
Mathematical Expeditions Reinhard Laubenbacher,David Pengelley Ingen forhåndsvisning tilgjengelig - 2014 |
Mathematical Expeditions: Chronicles by the Explorers Reinhard Laubenbacher,David Pengelley Ingen forhåndsvisning tilgjengelig - 1998 |
Vanlige uttrykk og setninger
aggregate algebraic analysis angle sum Archimedes arithmetic Axiom Axiom of Choice called Cantor Cardano cardinal number Cauchy Cauchy's Cavalieri's century coefficients complex numbers Continuum Hypothesis cube curve definition divisor elements equal equations of degree equivalent Euclid Euclid's Euclid's Elements Euclidean Euclidean geometry Euler Exercise exponent factors Fermat equation Fermat's Last Theorem FIGURE finite follows formula functions Fundamental Theorem Galois Gauss Germain given Greek hyperbolic geometry Hypothesis indivisibles infinite sets infinitesimal Lagrange Legendre Leibniz Lemma Lobachevsky mathematicians mathematics method natural numbers non-Euclidean non-Euclidean geometry number theory one-to-one correspondence parabola parallel postulate perpendicular PHOTO Poincaré polynomial prime numbers problem proof proposed equation Proposition prove Pythagorean triples Quadrature rational numbers real numbers reduced equation relatively prime result right angles roots segment set theory sides solution solve square straight line tangent triangle FDC values variable Zermelo's