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Newman J.R. (ed.) — The World of Mathematics, Volume 4
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Название: The World of Mathematics, Volume 4Автор: Newman J.R. (ed.) Аннотация: Volume 4 of a monumental 4-volume set covers such topics as mathematical machines, mathematics in warfare, a mathematical theory of art, mathematics of the good, mathematics in literature, mathematics and music, and amusements, puzzles, and fancies. Individual contributions by A. M. Turing, Aldous Huxley, Sir James Jeans, Lewis Carroll, and other notables. Informative commentary by noted mathematics scholar James R. Newman precedes each essay. Numerous figures.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2000Количество страниц: 448Добавлена в каталог: 07.04.2008Операции: Положить на полку |
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Probability and Induction (Kneale) 1449 Probability and Induction (Kneale), quoted 1451 fn. Probability and Its Engineering Uses (Fry) 1448 fn. Probability, addition, rule for 1341 Probability, calculus of 1329—1333 1381 1392 1393 1403—1404 1405 1407 1450 1450 Probability, character 1335 Probability, classic view 1395 Probability, compound event 1330 Probability, conceptualistic theory 1342—1343 1345 1346—1347 1348 1350 1354 Probability, consequences 1341 1344 Probability, curves 1391 Probability, dice throwing 1342 Probability, diminution 1330 Probability, ethical theory 1361 Probability, events to causes 1331—1332 Probability, formation of belief 1345—1346 Probability, frequency theory 1357 1406—1409 1411 1413 Probability, indeterminate 1347 Probability, indifference, principle of 1362 Probability, law of 1390 Probability, limited independent variety 1357 Probability, material proposition 1404 Probability, materialistic theory 1342—1343 Probability, mathematical expectation 1363 1363 1364 1365 1366 1367 1368 Probability, mathematical theory 1395 1463 Probability, matter of fact 1342 Probability, meaning 1398—1414 Probability, multiplication, rule for 1341 Probability, numerically measurable 1363 1364 Probability, Principles of the Theory of (Nagel) 1449 fn. Probability, propositions involving 1404—1405 Probability, rational acting hypothesis 1360 Probability, statistical 1266 1396 1484—1485 Probability, Statistics and Truth (von Mises) 1451 fn. 1618 Probability, study of 236 Probability, term 1399—1400 Probability, the Foundation of Eugenics (Galton) 1372 Probability, theory of 1156 1157 1207 1322 1334 1395 Probability, Theory of (Jeffreys) 1257 Probability, Treatise on (Keynes) 1356 1357 1448 Probability, weight and risk coefficients 1366—1367 Problems see also “Puzzles” Problems, arithmetical restorations 2439—2443 Problems, cat and grain 175—178 Problems, cattle problem 105—106 116 188 197—198 207 418 Problems, loaves and men 172—174 Problems, Mother Goose rhyme 178 Problems, Rhin papyrus 79 171—178 Problems, seven seven’s 2444—2448 Problems, solution, binary system 2423—2424 Problems, spider and fly 2433—2434 Process and Reality (Whitehead) 398 Proclus, Euclid 189 190 Proclus, parallel postulates 1649 Proclus, Pythagorean mathematics 1773 fn. Proclus, quoted 96 Proctor, Richard 2461 Progression, arithmetical and geometrical 123 Progression, harmomcal logarithms 137 Projectile, curved path 760 Projectile, fire arms, speed of 764 Projectile, motion of 755—770 Projectile, path of 729—730 734 Projectile, semi-parabolic path 755—758 Projection and section 623—639 Projection, method of 134 Projection, motion 755 Projection, parallel 606 Projective geometry, analytical 638 Projective geometry, creation 359 Projective geometry, Desargues’ theorem 627—628 629 631 Projective geometry, Desargues’ theorem, dual statement of 635 Projective geometry, duality, principle of 634—638 Projective geometry, Euclidean geometry, relationship 638 640 Projective geometry, Kepler 133 Projective geometry, neglect 631 Projective geometry, new theorems, discovery 638 Projective geometry, parallel lines 628—629 634 Projective geometry, Pascal’s theorem 629—630 631 Projective geometry, Pascal’s theorem, dual statement of 637 Projective geometry, perspective 107 Projective geometry, points 1706 Projective geometry, porisms 102 Projective geometry, sections, common geometrical properties 626 Prolate cycloid 1940 Prolixity, mathematics 38 Proof, analytical method 16 Proof, binomial theorem 299 Proof, by congruence 650 Proof, rules of 1930 Properties, measurable 1801—1802 1803 Prophecies of Daniel and the Apocalypse of St. John, Observations upon (Newton) 274 Proportionality, triangle 18 Proportions, mechanics 50 Proportions, notion 82 Proportions, theory of 99 191 525 Proportions, two mean lines of 181 Propositional function 70 1870—1871 1873 1895 1910 Propositions, calculus of 1307 Propositions, logic 1869—1870 Propositions, self-evident 1578 Propositions, true 11 Prospectiva pingendi, De (Francesca) 606 Proteins, structure 878 Protons, electrons 415 1075 Protons, positively charged 686 Przibram, Karl 1044 fn. 1045 1045 1046 Pseudospherical space 657 660 662 663 Pseudospherical surface 652—654 Psychology, A History of Experimental (Boring) 1147 1171 Psychology, measurement 1146—1147 Psychophysics 1152 1153 1155 1156—1166 1345 Psychophysik, Elemente der (Fechner) 1149 1153 1154 1156 1163 Ptolemy of Alexandria, Almagest 109 Ptolemy of Alexandria, cartography, scientific 780 Ptolemy of Alexandria, circular motion 96 Ptolemy of Alexandria, earth, measurement 792 Ptolemy of Alexandria, epicycles 1295 Ptolemy of Alexandria, founder of Alexandria library 100 Ptolemy of Alexandria, Harmonics 232 Ptolemy of Alexandria, planetary motion 109 110 1204 Ptolemy of Alexandria, trigonometry 18 Pulley, compound, Archimedes’ 181 187 Pure geometry 151 152 2034—2035 Pure Mathematics, A Course of (Hardy) 2024 Pure mathematics, discovery 1576 Pure mathematics, logic 1577 Pure mathematics, progress, nineteenth century 413 Pure mathematics, science of 402 Pure Mathematics, Synopsis of (Carr) 166 Pure strategy 1273 1288 Putter, A. 1029 fn. Puzzle book, Bachet’s 2416—2417 Puzzles see also ““Pastimes of Past and Present Times” (Kasner and Newman)” “problems” Puzzles, artisans, occupations 2417 fn. Puzzles, ferrying across a river 2418 Puzzles, relationships 2434—2435 Puzzles, rings removed from bar 2425 Puzzles, three jars problem 2419 Puzzles, Tower of Hanoi 2425—2426 Pyramid, characteristic shape of fire 96 Pyramid, volume of 94—95 169 175 Pyramids, golden section 80 Pyramids, measurement 12 82 Pyramids, plans and models 79 Pyrite crystals, dodecahedron 720 Pyrocollodion 931 Pythagoras, abstractions 416 Pythagoras, biography 82 1763 Pythagoras, comments by Diogenes Laertius 189 Pythagoras, foundations of geometry and arithmetic 90 Pythagoras, fraction of square of two 1058 Pythagoras, geometry 14 189 876 878 Pythagoras, incommensurable quantities 16 17 Pythagoras, irrationals 87 97 Pythagoras, justice, definition 2184 2198 Pythagoras, mathematical entities 409 Pythagoras, musical scale 85 189 2183 2183 Pythagoras, number, optical symbol 2323 Pythagoras, numbers, status of 408 Pythagoras, patterns and arrangements 163 Pythagoras, proportion, theory of 525 Pythagoras, ratios, equal 99 Pythagoras, right-angled triangle 188 190—192 408 Pythagoras, space-filling figures 86 Pythagoras, stratification 95 Pythagoras, theorems 2031—2032 2033 Pythagoras, unity of occasion 408 Pythagoras, vibration, law of 2297 Pythagoreans, Order of the, mathematics 1113 fn. Pythagoreans, Order of the, motto 189 Pythagoreans, Order of the, numbers 506 2016 2322 Pythagoreans, Order of the, philosophy 841 Pythagoreans, Order of the, spherical shape 672 Pythagoreans, Order of the, symbol 83 88 125 2324 Quadrant, Picard’s 792 Quadratic equations 29 86 88 89 91 115 116 249 253 350—351 1087 1089 Quadratic reciprocity, law of 301—302 310 325 Quadratrix curve 91 Quadratures, inverse of tangents 55 Quadratures, method of 40 90 2329 Quadrivium of knowledge 86 Qualitative postulates 1296 Quantics 355 1299 Quantifiers, universal and existential 1880 1906—1908 Quantity, space measurement 655 664 Quantity, symbol for 24 Quantum jumps 973 fn.—914 fn. 977—978 quantum mechanics 77 362 396 977 983 1047 1050 1298 Quantum physics, wave laws 686 Quantum theory 146 414—415 2062 2467—2468 Quantum theory, groups 1559 Quantum theory, heredity 975—995 Quantum theory, methods 1054—1055 Quantum Theory, The Physical Principles of (Heisenberg) 1049 Quantum theory, wave-mechanics 1074 Quantum-mechanical evidence 975—982 Quartic curves 113 Quartic equation 119 Quaternions 76 161 162 163 164 332 396 Questions, topological 570—571 Quetelet, Lambert A., deviation from an average 1182 Quetelet, Lambert A., error, law of 1157 Quetelet, Lambert A., inductive reasoning 1348 Quetelet, Lambert A., Probabilities, Letters on 1181 1183 Quincke, Georg Hermann 1032 Quine, W.V. O,, Mathematical Logic 1628 fn. Quintic curves 113 Quintic equation 119 Quipus, computers 463 Quotient, differential 47 61 Radiation, electromagnetic 219 Radiation, metals (table) 847 Radiation, negative terminal, source of 854 Radicals 2004—2005 Radiolarians 708 720 Radius vector 218 Radius, abstract idea 14 Rado, T., Plateau’s problem 888 902 Raindrops, distribution 1385 Raindrops, surface tension 1032 Ramachandra Rao, R. 367 Ramachandra Rao, R., quoted 369 Ramanujan, Srinivasa see also ““Srinivas Ramanujan” (Newman)” Ramanujan, Srinivasa, analytic theory of numbers 374 Ramanujan, Srinivasa, Collected Works 367 Ramanujan, Srinivasa, commentary on 366—367 Ramanujan, Srinivasa, complex multiplication 371 374 Ramanujan, Srinivasa, continued fractions 374 Ramanujan, Srinivasa, divergent series, theory of 369 370 Ramanujan, Srinivasa, elliptic integrals 369 Ramanujan, Srinivasa, Hardy, partnership with 2024—2025 2037 Ramanujan, Srinivasa, hypergeometric series 369 Ramanujan, Srinivasa, induction 166 Ramanujan, Srinivasa, letter to G.H. Hardy, quoted 370 Ramanujan, Srinivasa, modular equations 374 Ramanujan, Srinivasa, partitions of n 167 Ramanujan, Srinivasa, partitions, congruence properties of 375 Ramanujan, Srinivasa, prime numbers 371 Ramanujan, Srinivasa, theorems 370—373 Ramanujan, Srinivasa, Zeta-function 374 Ramanujan, Srinivasa, “Bernoulli’s Numbers, Some Properties of” 370 Ramsay, Frank Plumpton 1950 fn. Ramsay, Frank Plumpton, quoted 1980 Ramsay, William 920 927 928 Randomization, test of significance 1516—1518 Raphael, “School of Athens” 623 625 626 Rashevsky 1041 fn. 1300—1301 1309 Rashevsky, Mathematical Biology of Social Behavior 1299 Rashevsky, Mathematical Theory of Human Relations 1299 Ratio, black and white balls (pebbles) 1327—1328 1454 Rational economic behavior 1267 1268 Rational Indices, Law of (Hauy’s Law) 874 876 880 Rational numbers 326 511 513 525 528 Rational primes 512 Rational reality, numbers 85 Rationals, ratios 64—65 Ratios, equal 99 117 Ratios, relations 65 Rauber, A. 1008 fn. Rayleigh, Lord, acoustics 865 Rayleigh, Lord, bird color 1028 fn. Rayleigh, Lord, gases, work with 927—928 Rayleigh, Lord, liquid froth 891 Rayleigh, Lord, nitrogen density, measurements 1473 Rayleigh, Lord, oil films 1040 Rayleigh, Lord, soap bubble, breaking 895 896 Rayleigh, Lord, surface tension 892 Rays, Account of a Theory of Systems of (Hamilton), quoted 161 Reade, Winwood, quoted 553 Real numbers 34 50 63 65 96 534—536 1839 Reality and fiction, distinction 1336 Reasoning, calculus of 1861 Reasoning, chains of 6 42—43 Reasoning, kinds 1347 Recession, systematic motion of 1074 Rechts-links problem 686 fn. Reciprocants, differential invariants 363 Reciprocation, duality 112 121 Recorde, Robert, algebra, introduction into England 23 Recorde, Robert, commentary on 210—211 Recorde, Robert, “Declaration of the Profit of, Arithmeticke” 212—217 Recreational mathematics 2416 Recreations mathematiques et problemes des temps anciens et modernes (Ball) 243 fn. Rectangle, area 174 Rectangle, measuring 12 Rectilinear motion, uniform 51—52 Rectilinear triangle, angles 551 Recurrence, importance 411 Redefinition, numbers 28 Reducibility, axiom of 1953 Reductio ad absurdum 89 2031 Reduction and cancellation, science of 117 Reduction and restoration, algebra 23 Reed, Lowell J. 1416 Reflection, congruence 696 699 Reflection, sound 862 Reflexive symmetry 699 Refraction, law of 226 Regnault, Henri Victor 914 922
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