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Gullberg J. — Mathematics: from the birth of numbers
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Название: Mathematics: from the birth of numbersАвтор: Gullberg J. Аннотация: A gently guided, profusely illustrated Grand Tour of the world of mathematics. This extraordinary work takes the reader on a long and fascinating journey — from the dual invention of numbers and language, through the major realms of arithmetic, algebra, geometry, trigonometry, and calculus, to the final destination of differential equations, with excursions into mathematical logic, set theory, topology, fractals, probability, and assorted other mathematical byways. The book is unique among popular books on mathematics in combining an engaging, easy-to-read history of the subject with a comprehensive mathematical survey text. Intended, in the author's words, "for the benefit of those who never studied the subject, those who think they have forgotten what they once learned, or those with a sincere desire for more knowledge," it links mathematics to the humanities, linguistics, the natural sciences, and technology. Contains more than 1000 original technical illustrations, a multitude of reproductions from mathematical classics and other relevant works, and a generous sprinkling of humorous asides, ranging from limericks and tall stories to cartoons and decorative drawings. Over 1000 technical illustrations and cartoons and drawings
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1997Количество страниц: 1110Добавлена в каталог: 22.11.2014Операции: Положить на полку |
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Предметный указатель
Symbol/symbols, ratio 110 Symbol/symbols, relation 101 Symbol/symbols, subtraction 102 Symbol/symbols, summation 105 Symbolic logic 215 Symbolic phase 101 Symmetric equations 329 Symmetric matrix 654 Symmetry, law of 132 Syncopated style 298 Syncopation phase 101 System, geocentric 894 Systeme International d’Unites 53 Systems of blocks of elements 198 Systems of equations 325 Systems of equations, graphic solution 933 Systems of trigonometric equations 526 S’choty 170 Table, standard normal distribution 985 Table, trigonometric values 476 Table, truth 220 Tangens hyperbolicus 534 Tangent 388 470 Tangent, curve 504 Tangent, derivative 695 Tangent, equation 688 Tangent, hyperbolic 534 Tangent, sphere 403 Tangent, trigonometric function 470 Tangents, law of 486 Tanh, derivative 702 Target row 663 Tarski, A. 160 Tartaglia, N. 114 316 Tautologies 225 Taylor, B. 768 Taylor, R. 334 Taylor’s series 767 Tendency, central 974 Tera 54 Term, absolute 309 Term, general, series 264 Term, linear 309 Term, quadratic 309 Terminal point, vectors 602 Terminating decimal fractions 76 Terms, negligible, method of approximation 925 Terms, series 264 Terms, similar 128 ternary 46 Tessellation 395 Test, d’Alambert’s 277 Tetragon 392 394 Tetrahedral numbers 292 Tetrahedron/tetrahedra 397 448 Tetrahedron/tetrahedra, formulas 450 Tetraktys 289 THALES, history of trigonometry 461 Thales, theorem of 430 Theorem/theorems 157 see "Law" "Rule" Theorem/theorems of algebra, fundamental 299 305 Theorem/theorems of arithmetic, fundamental 78 Theorem/theorems, binomial 140 Theorem/theorems, Branchion’s 434 Theorem/theorems, Cauchy’s mean-value 718 Theorem/theorems, Cavalieri’s 446 Theorem/theorems, Chebyshev’s 977 Theorem/theorems, chord 438 Theorem/theorems, concurrent lines 432 Theorem/theorems, concurrent points 432 Theorem/theorems, cones 452 Theorem/theorems, cube 450 Theorem/theorems, cylinders 452 Theorem/theorems, de Moivre’s 791 Theorem/theorems, Desargues’s 434 Theorem/theorems, diagonals/sides, parallelogram 438 Theorem/theorems, dodecahedron 451 Theorem/theorems, dual, projective geometry 434 Theorem/theorems, Euler’s characteristic 448 Theorem/theorems, Euler’s polyhedron formula 448 Theorem/theorems, factor 304 Theorem/theorems, Fermat’s last 333 Theorem/theorems, fundamental, arithmetic 78 Theorem/theorems, fundamental, calculus 748 Theorem/theorems, Heron’s formula 444 Theorem/theorems, icosahedron 451 Theorem/theorems, inclusion 528 Theorem/theorems, incompleteness 160 Theorem/theorems, Lagrange’s mean-value 716 Theorem/theorems, lines, concurrent 432 Theorem/theorems, mean-value 716 Theorem/theorems, mean-value, Cauchy’s 718 Theorem/theorems, mean-value, extended 718 Theorem/theorems, mean-value, generalized 718 Theorem/theorems, mean-value, Lagrange’s 716 Theorem/theorems, mean-value, restricted 717 Theorem/theorems, octahedron 450 Theorem/theorems, Pascal’s 434 Theorem/theorems, plane geometry 426 Theorem/theorems, points, concurrent 432 Theorem/theorems, prime number 80 778 Theorem/theorems, prisms 451 Theorem/theorems, Ptolemy’s 438 Theorem/theorems, pyramids 451 Theorem/theorems, Pythagorean 435 Theorem/theorems, Pythagorean number 332 Theorem/theorems, regular polyhedra 448 Theorem/theorems, remainder 303 Theorem/theorems, Rolle’s 716 Theorem/theorems, scalar product 614 Theorem/theorems, secant 439 Theorem/theorems, secant-tangent 439 Theorem/theorems, solid geometry 446 Theorem/theorems, spheres 452 Theorem/theorems, spherical segments 452 Theorem/theorems, spherical triangles 453 Theorem/theorems, tetrahedron 450 Theorem/theorems, Thales’ 430 Theorem/theorems, torus 453 Theorem/theorems, Vinogradov’s 81 Theory, group 301 Theory, of games 965 Theory, of relativity, general 904 Theory, of relativity, special 904 Theory, of sets 231 THOMAS of Sarzana 41 Thousand, etymology 27 Tiling 395 397 Time dilation 905 Topological equivalence 369 378 Topological transformation 369 378 topology 377 378 Torricelli, E. 674 Torus 405 Torus, formula 453 Torus, surface, chromic number volume 884 Tower of Hanoi 285 Trace, matrix 641 Trajectory 1012 Transcendental functions 349 Transcendental functions, derivatives 695 Transcendental functions, expansion 771 Transcendental numbers 85 Transfinite numbers 257 Transfinite numbers, algebra of 261 Transformation, synonym of function 336 Transformation, topological 369 378 Transformations, Lorentz 904 Transforming, double integrals 887 Transforming, orthogonal/polar coordinates 887 Transitive, law 132 Translation, axes, volume 882 Translation, orthogonal coordinates 572 Transpose matrix 654 Transposition, cyclic permutation 192 Transversal 387 Trapezium 394 Trapezium, area 442 trapezoid 394 Trapezoid, area 442 Trapezoidal rule 949 Trapezoidal rule, boundary estimation 952 Trapezoidal rule, boundary formula 952 Trapezoidal rule, convergence 952 Tree diagram 186 TRENCHANT, J. 146 Trial 4 Triangle law, vectors 603 Triangle/triangles 392 Triangle/triangles, area 441 552 Triangle/triangles, area, determinants 653 Triangle/triangles, area, Heron’s formula 444 Triangle/triangles, area, trigonometric method 489 Triangle/triangles, circumcenter 432 Triangle/triangles, congruent 427 Triangle/triangles, Egyptian 393 Triangle/triangles, equilateral, Euclidean construction 415 Triangle/triangles, golden 419 Triangle/triangles, height 393 439 Triangle/triangles, isosceles, Euclidean construction 415 Triangle/triangles, nine-point 433 Triangle/triangles, Pascal’s 140 Triangle/triangles, Sierpinski 631 Triangle/triangles, similar 427 Triangle/triangles, spherical 404 Triangle/triangles, theorems 427 Triangle/triangles, types of 392 393 Triangular matrix 641 Triangular numbers 289 Triens 16 Trifolium 858 Trigonometric equations 516 Trigonometric equations, systems of 526 Trigonometric functions, complementary angles 471 Trigonometric functions, conversion table 475 Trigonometric functions, fundamental, derivatives 695 Trigonometric functions, graphs 502 Trigonometric functions, inverse, derivatives 697 Trigonometric functions, principal values 506 Trigonometric functions, substituting for algebraic expressions 738 Trigonometric functions, supplementary angles 474 Trigonometric functions, values, table 476 Trigonometric identities 507 Trigonometric identities, integration 727 Trigonometric products, breaking up 514 Trigonometric values, calculators 476 Trigonometric values, table 476 Trigonometry 457 Trigonometry, history 458 461 467 Trinomial 128 Triple/triples, integral 753 Triple/triples, products 622 Triple/triples, Pythagorean 332 Trirectangular 404 Trisection of an angle 423 Trivium 870 Troy-town 546 Truncation 164 Truth, table 220 Truth, value 220 Tsu Ch’ung-Chih 91 Tuple 188 Turing, A.M. 218 301 Twelve, etymology 27 Twelve-color map problem 204 Twin, cube 455 Twin, primes 81 Two-point, equation 553 Two-value principle 220 Type I error 970 Type II error 970 Ulam, S.M. 968 Uncertainty principle, Heisenberg’s 906 Uncia 16 Unconditional inequality 109 312 Undamped oscillations 1009 Undefined forms, limits 362 Undenary 46 Undetermined coefficients, method of 1027 Unendlichkeit, eine messbare 30 union 238 Unit, distance 71 Unit, fractions 126 Unit, imaginary 71 87 Unit, matrix 641 Unit, vectors 607 Unit, vectors, scalar products 615 Unitary matrix 658 Universal quantifier 220 Universal set 235 Universe 235 Unknowns 114 Unrestricted integral 756 Upper triangular matrix 641 Valence 202 Valid digits 164 Vallee-Poussin, C.J. 80 778 Value/values, absolute 71 Value/values, approximated 161 Value/values, average 751 Value/values, boundary 166 Value/values, mean, integrated 751 Value/values, principal, trigonometric 506 Value/values, trigonometric functions, table 476 Value/values, truth 220 Van Ceulen, L. 92 van Roomen, A. 92 Vandermonde, A.-T. 639 Variable/variables, algebra 114 Variable/variables, dependent 336 Variable/variables, independent 336 Variable/variables, polynomial 128 Variable/variables, power, derivative 689 Variable/variables, random 971 Variance 976 Variation of constants, method of 1025 Variations, calculus of 673 681 Varignon, P. 580 Veblen, O. 370 379 Vector analysis 599 Vector analysis, history 600 Vector/vectors, acceleration 901 Vector/vectors, algebraic 641 Vector/vectors, components 608 Vector/vectors, matrix 641 Vector/vectors, product, components 618 Vector/vectors, products 617 Vector/vectors, quantity 602 Vector/vectors, triple product 623 Vector/vectors, velocity 901 Vectorial angle 576 Velocity 896 Velocity, as electric current 1011 Velocity, average 897 Velocity, instantaneous 897 Velocity, integration 900 Venn diagram 242 Venn, J. 242 Vertex/vertices, angle 388 Vertex/vertices, concurrent 434
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