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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
Numeration system/systems, Akkadian 36 Numeration system/systems, Arabic 48 Numeration system/systems, Arabic, ancient 36 Numeration system/systems, Attic 36 Numeration system/systems, Aztec 60 Numeration system/systems, binary 62 Numeration system/systems, duodecimal 61 Numeration system/systems, Egyptian 34 Numeration system/systems, Greek 36 Numeration system/systems, Hebrew, ancient 36 Numeration system/systems, Herodianic 36 Numeration system/systems, hexadecimal 64 Numeration system/systems, Hindu-Arabic 48 Numeration system/systems, Ionic 36 Numeration system/systems, Mayan 58 Numeration system/systems, octal 64 Numeration system/systems, Roman 39 Numeration system/systems, sexagesimal 56 Numeration system/systems, Sumerian 35 Numeration system/systems, vigesimal 58 Numerator 74 Numerical integration 947 NUNES, P. 596 NUNEZ SALACIENCE, P. 596 Oblate ellipsoid 405 Oblique, cone 402 Oblique, cylinder 401 Oblique, prism 400 Oblong numbers 291 Obtuse, angle 388 Obtuse, triangle 393 Octagon 392 octahedron 397 448 Octahedron, formulas 450 Octal 46 Octal numeration 64 Octenary 46 October 19 Odd functions, expansion 919 Odd-even identities 508 Odd/even functions 340 Old English number names 26 Old Norse number names 26 One-sided limits 358 One-sided surfaces 380 One-to-one functions 346 Op art 375 Open half-line 387 Open interval 111 Operational precedence 122 Operator 336 Opposite angles 389 426 Opposites, doctrine of 291 Optical art 375 Order, determinant 646 Order, differential equation 991 Order, matrix 640 Ordered components 241 Ordered sample 187 Ordinal numbers 5 Ordinary differential equations 991 994 Ordinary differential equations, first-order 994 Ordinary differential equations, second-order 1015 Ordinate 472 549 Origin 549 Origin, number line 71 Origin, vectors 602 Orthodrome 596 Orthogonal coordinate system 472 549 Orthogonal coordinate system, rotation 573 Orthogonal coordinate system, translation 572 Orthogonal matrix 657 Orthogonal trajectories 1012 Orthogonal/polar coordinate transformation 887 Oscillating motion 1008 oscillations 1008 Oscillations, damped 1009 Oscillations, forced 1010 Oscillations, harmonic 1008 Oscillations, undamped 1009 Osculation, point of 386 OTHO, V. 92 465 OUGHTRED, W. 104 109 110 OUGHTRED, W., slide rule 176 Outcomes, favorable/unfavorable 966 PACIOLI, L. 102 135 399 418 PAGANINI, N. 83 PAO CHHI-SHOU 214 PAPPUS (PAPPOS), history of calculus 674 PAPPUS (PAPPOS), history of geometry 366 PAPPUS (PAPPOS), Pappus’s and Guldin’s theorem 866 884 Papyri, Egyptian 98 Papyrus, Ahmes 98 Papyrus, Moscow 99 Papyrus, Rhind 98 297 parabola 406 562 Parabola, equations 563 568 589 Parabola, equations, parametric 589 Parabola, segment, area 442 Parabolic geometry 382 Parabolic spiral 581 Paraboloid 405 Paraboloid reflectors 432 Paradox, barber 236 Paradox, Cretian 219 Paradox, Epiminides’ 219 Paradox, liar 219 Paradox, Russell’s 235 Parallel circles, torus 405 Parallel line/lines 387 Parallel line/lines, equations 555 Parallel line/lines, Euclidean construction 414 Parallel line/lines, postulate 381 Parallelepiped 400 Parallelepiped, volume 446 Parallelogram law, Vectors 603 Parallels of latitude 491 Parameter, elimination 597 Parametric equations 586 Parametric equations, arc length 832 Parametric equations, area, surface of revolution 864 Parentheses 122 Parker, E.T. 195 Parmenides 218 Partial differential equations 991 Partial differentiation 710 Partial fractions 130 Partial fractions, use of, integration 745 Partial sums 271 Particular solution, differential equations 993 PASCAL, B., combinatorics 184 PASCAL, B., history of calculus 675 PASCAL, B., Pascal’s theorem 434 PASCAL, B., Pascal’s triangle 141 PASCAL, B., probability 963 Pascal’s theorem 434 Pascal’s triangle 140 Path, descent, most rapid 590 Paths, Euler 203 Paths, Hamilton 203 Peano axioms 157 Peano curve 635 PEANO, G., 233 PEANO, G., axioms 157 PEANO, G., Peano curve 635 Pearson, E. 965 Pearson, K. 964 Peet, T.E. 99 Pell number sequence 288 Pell, J. 288 Pendulum property 591 PENROSE, L.S. 374 Penrose, R. 374 Pentacle 420 Pentadecagon, regular, Euclidean construction 416 Pentagon 392 Pentagon regular, Euclidean construction 415 Pentagonal numbers 291 Pentagram/pentagrams 420 Pentagram/pentagrams, magic 213 Perfect numbers 82 Perimeter 390 Perimeter, snowflake curve 627 Periodic decimal fractions 76 Periphery, definition 390 permutations 188 Permutations, all elements distinct 189 Permutations, cyclic 192 Permutations, identical elements 193 Perpendicular line/lines 387 Perpendicular line/lines, equations 555 Perpendicular line/lines, Euclidean construction 414 Perspective, focused 372 Peta 54 Phase, rhetorical 101 Phase, symbolic 101 Phase, syncopation 101 Phoenician alphabet 10 Phonetic alphabet 10 Pi, 85 89 920 Pi, 95 Pi, 94 pico 54 PinT 409 PITISCUS, B. 458 459 465 Pivot, entry 662 Pivot, operation 662 Pivoting, matrix 662 Place-value notation 32 Planar 376 Plane angle, definition 388 Plane geometry, definition 376 Plane geometry, theorems 426 PLATO (PLATON), Achademya 364 PLATO (PLATON), calculus 674 PLATO (PLATON), PLATO of Tivoli 463 PLATO (PLATON), Platonic solids 398 Platonic solids 397 398 Plus symbol, Rhind Papyrus 99 Poincare, J.H. 158 369 382 POINCARE, J.H., calculus 682 Point-slope equation 553 Point/points, bifurcation 348 Point/points, cardinal 499 Point/points, concurrent, theorems 432 Point/points, critical 798 799 816 Point/points, decimal 75 Point/points, definitions 386 Point/points, inflection, functions 341 Point/points, of inflection, definition 388 Point/points, of osculation 386 Point/points, saddle 816 Point/points, salient 386 Point/points, stable (iteration of functions) 348 Point/points, stationary 798 Point/points, terminal vectors 602 Poisson, S.-D. 964 979 Polar angle 576 Polar coordinate system, arc length 835 Polar coordinate system, area 856 Polar coordinate system, plane 576 Polar coordinate system, space 582 Polar equations 578 Polar form, complex numbers 788 Polar grid 577 Pole, coordinate system 576 Polygon/polygons 392 Polygon/polygons, regular, Euclidean construction 415 Polygon/polygons, spherical 404 Polyhedron/polyhedra 396 Polyhedron/polyhedra, formula, Euler’s 448 Polyhedron/polyhedra, semi-regular 399 Polynomial/polynomials 128 Polynomial/polynomials, addition 129 Polynomial/polynomials, division 129 Polynomial/polynomials, equations 307 Polynomial/polynomials, functions 348 Polynomial/polynomials, multiplication 129 Polynomial/polynomials, prime 303 Polynomial/polynomials, root extraction 144 Polynomial/polynomials, subtraction 129 Poncelet, J.V. 367 434 Population growth 1000 POSITION 896 Position as electric charge 1011 Position, system, decimal 48 Position, vectors 608 positional notation 32 46 Postmultiplication 644 Postulate/postulates, definition 157 Postulate/postulates, Euclidean 381 Postulate/postulates, indefinite continuation of straight line 381 Postulate/postulates, non-Euclidean 381 Postulate/postulates, parallel 381 Pound, U.S., definition 52 Power series 765 Power series expansion, 792 Power series expansion, 773 Power series expansion, binomial 775 Power series expansion, cosine of x 773 Power series expansion, integration by 746 Power series expansion, natural logarithms 773 Power series expansion, roots 776 Power series expansion, sine of x 771 Power series expansion, transcendental functions 771 Power series, convergence 766 Power sets 238 Power/powers 134 Power/powers, calculation rules 136 Power/powers, complex numbers 791 Power/powers, functions 350 Power/powers, functions, integrating 723 Power/powers, history 134 Power/powers, indeterminate 785 Power/powers, matrices 644 Power/powers, variable, derivative 689 Precedence, operational 122 Predicate logic 216 Preferred numbers 929 Premise 157 Premise, major 227 Premise, minor 227 Premultiplication 644 Prime/primes 77 Prime/primes, factor 303 Prime/primes, Mersenne 79 Prime/primes, number theorem 80 778 Prime/primes, numbers 77 Prime/primes, polynomial 303 Prime/primes, pseudo- 80 Prime/primes, testing method of Fermat 80 Primitive integral 722 Principal diagonal, determinant 646 Principal diagonal, matrix 641 Principal minor 648 Principal values, trigonometric functions 506 Principle of contradiction 216 Principle of detachment 223 Principle of excluded middle 216 Principle of identity 216
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