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Newman J.R. (ed.) — The World of Mathematics, Volume 4
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Íàçâàíèå: The World of Mathematics, Volume 4Àâòîð: Newman J.R. (ed.) Àííîòàöèÿ: 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.
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Bilateral symmetry, human body 671 674 686—687 Bilateral symmetry, reflections or rotations 672 724 Billion, use of term 450 455 Binary digit 1307 Binary scale 122 516—517 2423 Binary theory 310 2422 Binomial congruence 310 311 325 Binomial equation 310 Binomial theorem 139 140 256 258 299 519—524 Biological sciences 413 Biologist, socialism, problem of 956 Biology, evolution, theory of 2359—2360 Biology, fibers, study of 691 Biology, mathematical 1299 Biology, similitude, principle of 1004 Biology, The Axiomatic Method (Woodger) 1660 fn. Biot, Jean Baptiste 275 837 1324 Biquadratic reciprocity 325 Birds, ability to count 433 434 488—496 Birds, air currents, use of 1023—1024 Birds, flight speed 1017—1019 1020 1021—1022 Birds, flying, size relation 955 Birds, gifted 488—489 Birds, optical colors 1028 Birds, relative proportions 1002 fn. Birds, self-conditioning 490 Birds, The Flight of (Headley) 1019 fn. Birkhoff, George David, Aesthetic Measure 671 fn. Birkhoff, George David, Algebra, Modern, A Survey of 1625 fn. Birkhoff, George David, commentary on 2182—2184 Birkhoff, George David, minimax problems 889 Birkhoff, George David, Relativity and Modern Physics 2183 fn. Birkhoff, George David, Relativity, Origin, Nature and Influence of 2183 fn. Birkhoff, George David, “Ethics, Mathematical Approach to” 2198—2208 Birkhoff, George David, “Mathematics of Aesthetics” 2185—2195 Bishop, John 1016 fn. Bismuth, discovery 923 Bit, binary digit 1307 Bjerknes, Vilhelm 1032 Black and white, ratio 1327—1328 1454 Black, Joseph 1322 Blackboards, arithmetic 460 Blacker, C.P., Eugenics, Galton and After 1169 fn. Blaeu, Willem, longitude inventions 782 Blake, William, quoted 671 1901 1956 2223 Bliss, G.A. 889 Blondel, Francois 616 Blood transfusion, Cassini’s experiments 790 Blundeville, Thomas 803 Bode, Johann Elert 221—222 fn. Bode’s law 221 313 825 Body size, upper and lower limitations 1036 Body, moving down inclined plane 729 740—742 746—747 Boehm-Bawerk, Eugen, interval of indeterminacy 1281 1283 Boehme, Jacob 273 Boethius, Anicius 18 Bohr, Niels, complementarity 1049 1053—1055 Bohr, Niels, spectral lines 1064 Bolivia, numeral words 432 Bologna, Italy, center of learning 118 Boltzmann constant 979 fn. 994 Boltzmann, Ludwig 275 1591 Boltzmann, Ludwig, ergodic hypothesis 2182 Bolyai, John, hyperbolic geometry 1639 Bolyai, John, non-Euclidean geometry 639 2020 Bolyai, Wolfgang 158—159 Bolzano, Bernhard, continuous function 2411 2413 Bolzano, Bernhard, intuition 1971 Bolzano, Bernhard, Paradoxes of the Infinite 2411 Bolzano, Bernhard, probability 1396 Bolzano, Bernhard, velocity, moving point 1959 Bonner, John Tyler 996 fn. Bonnet, Charles, spirals 718 Bookkeeping, use of Roman numerals 451 Boole, George, commentary on 1854 Boole, George, invariants 349 350 351 Boole, George, logical algebra 163 397 1870 1894 Boole, George, Mathematical Analysis of Logic, The 1679 1856—1858 Boole, George, quoted 1867 Boole, George, symbolic logic 1862 1864—1868 Boole, George, Thought, Laws of 1576 1853 Boolean algebra 1868—1871 Boredom, coefficient of 1169 Borelli, Giovanni Alfonso 1012 1013 1022 1023 Borelli, Giovanni Alfonso, quoted 891 Borelli’s law 1013 Boring, Edwin Garrigues, biography 1147 Boring, Edwin Garrigues, Experimental Psychology, A History of 1147 1171 Boring, Edwin Garrigues, “Gustav Theodor Fechner” 1148—1166 Born, Max, quantum mechanics 396 Boss Puzzle 2429—2432 Bosse, Abraham 631 Bothwell, Adam 121 Bottomley, Gordon, quoted 2070 Boundary, abstract principles 2345 Bourdelin, Claude 786 Boutroux, Etienne E. MM Science et Religion 2047 Bouts, Dirk, Last Supper 604 605 Bouvard, Alexis, Uranus, positions 823 831 Boveri, Theodor 1034 1035 Bowditch, Nathaniel 1321 Boycott, A.E. 1036 fn. Boyer, Carl B., Analytic Geometry, Invention of 236 fn. Boyer, Carl B., Calculus, The Concepts of the 286 fn. 287 Boyle, Robert 272 Boyle’s law 880 Boys, C. Vernon, earth, weighing 884 884 Boys, C. Vernon, quoted 886 Boys, C. Vernon, Soap Bubbles: Their Colours and the Forces Which Mould Them 884 fn. Boys, C. Vernon, “Soap-bubble, The” 891—900 Brachistochrone problem 267 Brackets, symbol 27 Bradley, Francis Herbert 387 Bradley, James 809 811 814 823 Bragg, William Henry, commentary on 851—853 Bragg, William Henry, Light, The Universe of 852 Bragg, William Henry, Physical Sciences, The 1048 fn. Bragg, William Henry, uncertainty principle 1048 Bragg, William Henry, X-rays and crystals 842 852 Bragg, William Henry, “Rontgen Rays” 854—870 Bragg, William Lawrence 842 845 Bragg, William Lawrence, Crystalline State, The 851 fn. Brahe, Tycho, astronomical speculations 120 Brahe, Tycho, astronomy, observational labors 728 Brahe, Tycho, celestial measurements 218 Brahe, Tycho, Kepler, association with 125—126 223—225 Brahe, Tycho, logarithmic tables 123 Brahe, Tycho, planetary motion 1204 Brahe, Tycho, Rudolphine tables 225 232 Brahe, Tycho, telescope 792 Brahmagupta 78 117 Brain, weight related to body weight 956 Brainwaves, wordless 495 Bramante, Donato 609 1005 Brandt, Hennig, phosphorus 923 Brazil, finger counting 435 Brazil, forest tribes’ number knowledge 432 Breeder, C.M. 1024 fn. Breslaw, Germany, mortality tables 1416 1419 1437—1439 1446 Breton, Elie le 1011 fn. 1032 Brewster, David 281 339 Brewster, David, quoted 234 Brianchon, Charles, projective geometry 631 Brianchon, Charles, theorem 637 Bridgeman, P.W., Dimensional Analysis 1004 fn. Bridgeman, P.W., Logic of Modern Physics, The 2349 fn. Bridgeman, P.W., mathematical reality 2349 Briggs, Henry 123—124 125 140 Brinton, D.G. 432 fn. Britain, naval tactics, Battle of Trafalgar 2154—2157 (see also “England”) British Museum, Rhind papyrus 169 170 British Scientists of the Twentieth Century (Crowther) 2274 fn. Broad, C.D. 280 395 398 Broglie, Louis Victor de 974 Bromwich, Thomas John I’Anson, commentary on 2449 Bromwich, Thomas John I’Anson, Infinite Series, The Theory of 2449 Bromwich, Thomas John I’Anson, “Easy Mathematics and Lawn Tennis” 2450—2454 Bronowski, J., operations research 2159 Bronowski, J., “Can Machines ‘Think’?” 2067 fn. Brooke, Rupert, quoted 358 fn. Brouncker, William, Viscount 137 138 Brouwer, Luitzen E.J., intuitionism 1747—1749 1751 2058 Brouwer, Luitzen E.J., map, boundary points 1968 Brouwer, Luitzen E.J., paradoxes 167—168 Brouwer, Luitzen E.J., reducibility, axiom of 1953 fn. Brown, Lloyd A., Cassini, Jean Domenique 795 fn. Brown, Lloyd A., Maps, The Story of 778 fn. 779 Brown, Lloyd A., “Longitude, The” 780—819 Brown, Robert 1043 1044 Browne, Sir Thomas, quoted 368 871 Browne, Sir Thomas, symmetry in nature 712 Brownian movement 1043—1045 1046 1392 2010 Brownlee, J. 1045 fn. Bruecke, Ernest 642 Brunelleschi, Filippo 605 Bruno, Giordano 2327 fn. Brunswick, Carl Wilhelm Ferdinand, Duke of 156 300 306 307 317—318 321 Bryan, G.H. 1019 fn. Buchler, Justus 1772 Buff on, Georges L.L., coin tossing, table 2381 Buff on, Georges L.L., Political Arithmetic 1333 Buff on, Georges L.L., probability 1333 1372 Buff on, Georges L.L., quoted 1369 Buller, A.H.R. 1042 fn. Bullitt, John M., Jonathan Swift and the Anatomy of Satire 2213 fn. Bunsen, R.W., spectroscope 919 922 Buot, Jacques 787 Burgi, Joost, logarithms 125 Burials and Christnings, Bills of Mortality 1424 1426 Buridan, Jean, impetus, theory of 727 728 Burke, Edmund, quoted 1217 1452 Burnet, Thomas, quoted 785 Burning glasses, Archimedes’ 179 Bush, Vannevar, differential analyzer 2074 Butler, Bishop, quoted 1360 1362 1362 1398 1459 Butler, Dr. George 1178 Butler, Samuel, quoted 2041 2053 2252 Butterfield, Herbert, Science, Origins of Modern 726 fn. Buxton, Jedidiah, idiosavant 465 Buxton, Jedidiah, problems solved 468—470 477 Byron, Lord 329 Byron, Lord, quoted 1094 1294 1524 Cabbalists, mathematicians 2017 Cabot, Sebastian, longitude 781 Cairnes, John E. 1220 Cajori, Florian 286 fn. Calandri, arithmetic book 461 Calcul infinitesimal, Reflexions sur la mitaphysique (Caraot) 292 fn. Calculate, origin of word 456 Calculating machines see “Computing machines” Calculating prodigies, law for rapidity of mental work 486—487 Calculation see also “Counting” Calculation, approximative 508 Calculation, Mental 465 467 Calculation, numerical laws 1820—1822 Calculation, symbolism 28 calculus ratiocinator 1861 1862 Calculus, axioms 1682 Calculus, differential 42 47 54—55 129 132 139 142 143 152 258 887 2341 Calculus, infinitesimal 43 48 52 53—62 95 127 142 146 286—293 411 1581 2330 2343 Calculus, integral 42 47 90 103 104 135 139 142 143 258 Calculus, logic 1857 Calculus, origins 2056 Calculus, probability 1329—1333 1381 1392 1393 1403—1404 1405 1407 1450 1450 Calculus, sentential 1684—1685 1693 1741 1910—1913 1918 1921—1929 Calculus, tensor 328 641 Calculus, The Concepts of the (Boyer) 286 fn. 287 Calculus, variations 111 153 267 274 883 886—890 901 Calvert, E.R. 1261 fn. Cambridge University; Analytical Society 517 Cambridge University; Analytical Society, differential calculus 152 Cambridge University; Analytical Society, honors in mathematics 1174—1177 Cambridge University; Analytical Society, Leibniz’s notation 59 Cambridge University; Analytical Society, Sadlerian professorship of mathematics 353 Cambridge University; Analytical Society, women students 354 Camerarius, Joachim 671 fn. Camerarius, Joachim, quoted 601 Campani, telescopes 791 Campbell, Norman Robert, commentary on 1795 Campbell, Norman Robert, Physics, the Elements 1796 Campbell, Norman Robert, probability 1405 Campbell, Norman Robert, What Is Science? 1796 Campbell, Norman Robert, “Measurement” 1797—1813 Campbell, Norman Robert, “Numerical Laws and the Use of Mathematics in Science” 1814—1829 Cancellation and reduction, science of 117 Candolle, A.P. de 1007 Cannizzaro, Stanislao, unitary theory 914 922 Cannon, Walter 1318 Canonical binary forms 358 Cantor, Georg, cardinal, greatest 388 Cantor, Georg, infinity, mathematical theory 1583—1587 1592 1593 1998 2411 Cantor, Georg, mathematics, formalizing 1971 Cantor, Georg, sets, theory of 1593—1605 2057 Cantor, Georg, symbolic logic 1580 Cantor, Georg, theorem 2032 Cantor, Georg, transcendentals 514 Cantor, Georg, transfinite numbers 1674 Cantor, Moritz 572 fn. 601 Capillarity, laws of 1211—1212 Caraap, R., Logic and Mathematics, Foundations of 1628 fn. Caraot, L.N.M. 292 fn. 631 632 1383 2462 Caratheodory, C 1732 card tricks 2421 Cardan (Cardano), Girolamo, algebra 76 Cardan (Cardano), Girolamo, Ars Magna 119 Cardan (Cardano), Girolamo, biography 119 Cardan (Cardano), Girolamo, cubic equation 118 Cardan (Cardano), Girolamo, equations, algebraic theory 120 Cardan (Cardano), Girolamo, pentagon 615 Cardan (Cardano), Girolamo, probability, theory of 1395 fn. Cardinal numbers 389 1584 Carlyle, Thomas, quoted 128 1203 1378 Carpenter’s rule 84 Carr, George Shoobridge 366 fn. Carr-Saunders, A.M. 1261 fn. Carroll, Lewis (Charles L. Dodgson), Alice’s Adventures in Wonderland 2399; 2399 fn. Carroll, Lewis (Charles L. Dodgson), commentary on 2397—2401 Carroll, Lewis (Charles L. Dodgson), quoted 432 Carroll, Lewis (Charles L. Dodgson), Through the Looking Glass 1107—1114 1126 1886—1890 2348 2397 Carroll, Lewis (Charles L. Dodgson), “Hemispherical Problem, A” 2398 Carroll, Lewis (Charles L. Dodgson), “Knot IX” 2405—2409 Carroll, Lewis (Charles L. Dodgson), “Riddles” 2402—2409 Carroll, Lewis (Charles L. Dodgson), “Two Clocks, The” 2405 Carroll, Lewis (Charles L. Dodgson), “What the Tortoise Said to Achilles” 2402—2405 Cartel, economics 1277 1283 Cartesian oval 131 132 337 Carthage, acquisition of land 882 886 Cartography, scientific, beginning 780 785 Cassini, Giovanni Domenico (Jean Domenique), Academie Royale des Sciences 791 793 Cassini, Giovanni Domenico (Jean Domenique), biography 789 Cassini, Giovanni Domenico (Jean Domenique), blood transfusion experiments 790 Cassini, Giovanni Domenico (Jean Domenique), Ephemerides 791 793 Cassini, Giovanni Domenico (Jean Domenique), Holy Days, determination 790 Cassini, Giovanni Domenico (Jean Domenique), Jupiter’s satellites 790 Cassini, Giovanni Domenico (Jean Domenique), longitude surveys, instructions 796—798 Cassini, Giovanni Domenico (Jean Domenique), planisphere 794 Cassini, Giovanni Domenico (Jean Domenique), surveying 790 Cassini, Giovanni Domenico (Jean Domenique), timekeepers 799—800 Cassini, Jean Domenique (Brown) 795 fn. Cassirer, Ernst 1834 fn.
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