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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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Geometry, projective see “Projective geometry” Geometry, Projective (Veblen and Young) 1616 Geometry, pure and physical 152 1641—1644 2034—2035 Geometry, quoted 239—253 Geometry, replaced by algebra 1298 Geometry, revival 207 Geometry, rhetorical 130 Geometry, Rhind papyrus 174 Geometry, scientific method 647 Geometry, shape 1547—1548 Geometry, solid 14 568 Geometry, space 67 86 110 342 1547 Geometry, Thales’ 82 Geometry, The Axioms of (Helmholtz) 550 fn. Geometry, topology 570 Geometry, trigonometry separated frGeometry, The (Descartes) 26—27 31 32 237 520 Gerhardt, Charles Frederic 914 Germain, Sophie 325 332 333—334 Germanium, discovery 921 Germany, mathematics, rise of 118 120 Germany, mathematics, teaching reform 1832 Germany, number designation by knots 463 Ghiberti, Lorenzo 616 Gibbon, Edward, quoted 381 1373 Gibbs, Willard, statistical physics 994 Gibbs, Willard, surface tension 891 892 893 Gilbert, William Schwenck, quoted 937 1936 2385 Gilbert, William, magnetism and gravitation, theory of 728 Gilman, Daniel Coit 355 Ginsburg, Jekuthiel, Numbers and Numerals 430 Ginsburg, Jekuthiel, Numbers and Numerals, “From Numbers to Numerals” 442—464 Girard, Albert 23 Glaisher, J.W.L. 821 fn. Glanvill, Joseph, quoted 552 Gliding flight, aeronautics 1023 1024 Globular star-clusters, diameters 1039 1039 Gnomon, L-shaped border 84—85 Goedel number 1688—1692 Goedel, Kurt, axiomatic method 1668—1669 1849 Goedel, Kurt, Peano’s primitives 1626 fn. Goedel, Kurt, “Undecidable Propositions of Principia Mathematica and Related Systems” 1668 Goedel’s Proof 1615—1616 2059 2109 Goedel’s Proof, Principia Mathematica 1685—1695 Goethe, Johann Wolfgang von, Farbenlehre 2016 Goethe, Johann Wolfgang von, Faust 271—272 2329 Goethe, Johann Wolfgang von, mathematics 1754 2325 Goethe, Johann Wolfgang von, quoted 975 1034 1832 2320 Goethe, Johann Wolfgang von, spiral tendency in nature 718 Goethe, Johann Wolfgang von, tails of vertebrates 702 Goethe, Johann Wolfgang von, tree, height 1007 Gold, atomic weight 925—926 Goldbach, Christian 365 367 499 507 1686 2437 Golden section, Fechner’s paper on 1154 Golden section, Great Pyramid 80 Golden section, ladder of numbers 98 Golden section, star pentagram 88 Goldschmidt, Richard B., Understanding Heredity 934 fn. Golenischev papyrus 169 Gompertz, Benjamin 2373—2374 2376 Gonseth, F. 1743 1744 Goodeve, Sir Charles 1245 Goodness, organic nature of 1363 Googol 1953 fn. 2007—2010 Goths, alphabetic numerals 451 Gottschalk, E. 510 Goudsmit, Samuel A., Alsos 1050 fn. Gould, R.T. 817 Grafe, A. von 643 fn. Graham, George 808 808 809 811 Grammar, arithmetic needful for 214 Grant, Duncan 1356 1358 Grapes, fermenting (optically dextroactive) 689 Graph, configuration 572 Graphic representation 605 Grassmann, Hermann, Ausdehnungslehre 396 1649 Grassmann, Robert 293 fn. Gratry, Abbe 1353 Graunt, John, commentary on 1416—1418 Graunt, John, Natural and Political Observations made upon the Bills of Mortality 1416 1437 Graunt, John, “Vital Statistics, Foundations of” 1421—1435 Graves, L. M 889 Graves, Robert, “Dog Walking Ordinance” 1890—1893 Gravitation, astronomical phenomena 1319 Gravitation, Einstein’s theory 146 328 409 841 1077 1095 1096 1100 1101—1102 1103 Gravitation, electromagnetism 881 Gravitation, inverse square law 823 Gravitation, Newton’s law of 798 799 880 1094—1095 1096 1098 1100 1101 1103 1317 Gravitation, solar system 1004 1004 Gravity, animals affected by 1025 Gravity, form control 1038 Gravity, law of 62 111 142 144 145 146 256 257—258 266 268 315 548 798—799 880 1077 1080 1094—1104 Gravity, lessening influence 1038 Gravity, mass-energy 1030 Gravity, small animals 953 Gravity, surface-tension 1038 Greater Logic (Hegel) 387 Greatest common measure 16—17 101 Greek Geometry from Thales to Euclid (Allraan) 2324 fn. Greek Mathematics, A Manual of (Heath) 76 191 Greeks, algebra 13 16 Greeks, analytical geometry 236 Greeks, astronomy 14 Greeks, curvilinear figures 34 40 41 42 53 Greeks, eclipses, sun and moon 1839 Greeks, ellipse 229 Greeks, Euclidean construction 502 Greeks, fractions, reducing 12 Greeks, geometry 10 11 13 61 68—69 881 Greeks, incommensurable lines 26 528 Greeks, infinity, forbidden notion of 2324 2329 Greeks, irrational numbers 89 Greeks, logistica 498 Greeks, mathematics 18 89 116 188 2327 Greeks, motion, conception of 19 Greeks, notation 92 99 114—115 Greeks, number symbols 418 443 446 Greeks, numbers and magnitudes, distinction 17 61—63 Greeks, polyhedra, tabulation 723 Greeks, problems, classification 91 Greeks, projective geometry 632 Greeks, prolixity 38 Greeks, space 2340 Greeks, tangent to a curve 36 Greeks, triquetrum 714 Greeks, “symmetric,” use of word 720 Green, George 1320 Greene, Robert, quoted 489 Greenhili, George 1004 fn. 1006 1006 1019 1107 Greenhood, David, Down to Earth, Mapping for Everybody 779 fn. Greenwich (Richardson) 800 fn. Greenwich, London, mean time 778 1127 Greenwich, London, Royal Observatory 800 Gregg, R.B. 1253 Gregory, James 78 137 138 139 140 143 Gregory, R.P. 1035 fn. Griffin, Jonathan 1253 Griffiths, John 2373 Grimaldi, Francesco Maria, on nature of light 260 262 Gross, Mason 399 fn. Grosseteste, Robert 605 726 Grosseteste, Robert, and the Origins of Experimental Science (A.C. Crombie) 726 fn. Grote, George 1191 Ground of Artes, The (Recorde) 210—211 Groups, automorphisms 696 Groups, axiomatic concepts 1847 Groups, definition 1539 Groups, function theory 2346 Groups, relationships, numbers 402 Groups, simple 1999 Groups, system 1538—1543 Groups, theory 167 879 1376 1534—1573 Groups, transformation and invaria 1544—1546 2341 Groups, units, comparing 492 Growth and Form (Thompson) 708 884 996 998—1000 1030 Growth, rate of 1002 Gruppen von endlicher Ordnung, Theorie der (Speiser) 702 Guldin, Paul 111 Gulliver’s Travels (Swift) 26 1001—1002 1002 1003 1076 2210—2220 Guttman, Louis, Measurement and Prediction 1303 1305 1306 Habsburg lip 976 Hadamard, Jacques S., Mathematical Field, Psychology of Invention in the 2039 2351 Hadamard, Jacques S., prime number theory 158 507 Haddon, A. C 440 fn. Haeckel, Ernst, Challenger Monograph 708 720 Haeckel, Ernst, Kunstformen der Natur 707 Hahn, Hans, commentary on 1591—1592 Hahn, Hans, Vienna Circle 1935 Hahn, Hans, “Crisis in Intuition, The” 1942 fn. 1956—1976 Hahn, Hans, “Infinity” 1593—1611 Hahn, Hans, “Logik, Mathematik, und Naturerkennen” 1935 fn. Haldane, Elizabeth S. 235 fn. Haldane, J.B.S., Causes of Evolution, The 950 Haldane, J.B.S., commentary on 950—951 Haldane, J.B.S., On Being the Right Size 950 952—957 Haldane, J.B.S., quoted 1787 2012 Haldane, J.B.S., “Mathematics of Natural Selection” 958—972 Hales, Stephen 1033 fn. Hall, A.R., Scientific Revolution, The 126 fn. Hall, G.S., quoted 1148 Halley, Edmund, commentary on 1418—1419 Halley, Edmund, Jupiter and Saturn, motions 1317 Halley, Edmund, longitude problem 804 814 Halley, Edmund, Mortality of Mankind, Degrees of 1416 fn. Halley, Edmund, mortality tables, Breslaw 1416 1416 1419 1437 Halley, Edmund, Newton’s Principia 286 1418 Halley, Edmund, planetary motion 144 264 278 Halley, Edmund, publications 1418 Halley, Edmund, surveying 795 Halley, Edmund, variation, lines of 784 Halley, Edmund, “Life Insurance Tables, First” 1437—1447 Halley’s comet 144 1326 1419 2212 Halphen, Georges 363 Halsted, George Bruce 1375 Hambidge, J., Dynamic Symmetry 718 fn. Hamel, C, axioms of set theory 1732 Hamilton, William Rowan, algebraic discoveries 76 Hamilton, William Rowan, biography 161 Hamilton, William Rowan, Characteristic Function 161 162 164 Hamilton, William Rowan, dynamics, laws of 659 Hamilton, William Rowan, least action, principle 110 132 Hamilton, William Rowan, quaternions 76 162 163 164 332 Hamilton, William Rowan, Rays, Account of a Theory of, quoted 161 Hamilton, William Rowan, symbolic logic 1862—1863 Hankin, E.H. 1024 fn. Hansen, Peter Andreas, Neptune, discovery 837 Harcourt, William 1355 Hardy, Godfrey Harold, analytic theory of numbers 158 Hardy, Godfrey Harold, autobiography 2036—2038 Hardy, Godfrey Harold, commentary on 2024—2026 Hardy, Godfrey Harold, definite integrals 371 Hardy, Godfrey Harold, Littlewood, collaboration with 2024 2037 Hardy, Godfrey Harold, mathematical reality 2349 2353 2363 Hardy, Godfrey Harold, Mathematician’s Apology, A 1855 fn. 2027—2038 Hardy, Godfrey Harold, partitions of n 167 Hardy, Godfrey Harold, prime number theorem 508 Hardy, Godfrey Harold, Principia Mathematica 1855 Hardy, Godfrey Harold, Pure Mathematics, A Course of 2024 Hardy, Godfrey Harold, quoted 2138 Hardy, Godfrey Harold, Ramanujan 366 fn. 367 370—373 375 2024—2025 2037 Hardy, Godfrey Harold, Waring problem 515 Hardy’s law 2026 Hare, Maurice Evan, quoted 2070 Harmonic analysis 2297—2301 Harmonic mean 1489 1490—1491 1492 Harmonic progressions, civil life 127 Harmonices Mundi (Kepler) 126 127 Harmonics (Ptolemy) 232 Harmony of numbers 2322 harmony, applications 671 Harmony, Elements of (Aristoxenus) 192 Harriot, Thomas 23 29 Harrison, John, award for making marine chronometer withheld 814—819 Harrison, John, biography 807 Harrison, John, Copley medal 811 Harrison, John, escapement, grasshopper 808 809 Harrison, John, grandfather clocks 807 808 Harrison, John, gridiron pendulum 807 808 Harrison, John, marine chronometer 779 804 808 Harrison, John, sea trials, marine timekeepers 809—810 812 815 818 Harrison, Mr. John, The Case of 819 Harrison, R.G. 692 Harrison, William 812 813 815 819 Harrod, R.F. 1355 fn. Harrod, R.F., quoted 1203 1356 1359 Hartree, D.R. 2114 Hartshorne, Charles 395 fn. Hartsoeker, Niklaas 786 Hatchett, Charles 923 Hauey, Rene Just, atom, theory 873—874 Hauey’s Law 874 876 880 Haughton, Rev. Mr., cubical curves 918 Hausdorff, sphere, surface measurement 1944—1945 Haycraft, Howard 2221 fn. Headley, F.W., Birds, The Flight of 1019 Heap, symbol 12 Hearing, (table) 2303 Hearing, sensation of 2301—2302 Hearing, threshold of 2302—2304 Heart beats, animal 1025 Heart beats, atom 164 Heart, mammals, an asymmetric screw 687 Heat, statistical theory 979 Heath, Thomas, Archimedes, The Works of 181 fn. 197 198 Heath, Thomas, Euclid’s Elements, The Thirteen Books of 191 fn. 1647 Heath, Thomas, Greek Mathematics, Manual of 16 191 Heavenly Bodies, The Circular Motion of the (Cleomedes) 205 Heaviside, Oliver 1003 Heawood, four-color problem 591 Hebrews, numerals 451 Hegel, Georg Wilhelm Friedrich 314 316 387 Heiberg, Johan Ludvig 94 Heisenberg, Werner; biography 1050 Heisenberg, Werner; biography, quantum mechanics 362 396 1047 1050 Heisenberg, Werner; biography, Quantum Theory, The Physical Principles of 1049 Heisenberg, Werner; biography, uncertainty principle 1047—1055 Heisenberg, Werner; biography, wave mechanics 164 Heitler — London theory 977 978 983 985 Heitler, W. 977 Heliocentric theory, Copernicus 110 120 218 226 227 2327 Heliodorus of Larissa, perspective 605 Heliotrope, invention 327 Helium, discovery 919 927 Helmert, Frederick Robert, “Earth, Figure of the” 792 fn. Helmholtz, Hermann von, Axioms of Geometry, The 550 fn. Helmholtz, Hermann von, Axioms of Geometry, The, birds’ flight 1018 fn. Helmholtz, Hermann von, Axioms of Geometry, The, commentary on 642—646 Helmholtz, Hermann von, Axioms of Geometry, The, energy, conservation 643 Helmholtz, Hermann von, Axioms of Geometry, The, geometry, assumptions 550 Helmholtz, Hermann von, Axioms of Geometry, The, metaphysics 645 fn. Helmholtz, Hermann von, Axioms of Geometry, The, ophthalmoscope, invention 643 Helmholtz, Hermann von, Axioms of Geometry, The, Physiological Optics 643 644 Helmholtz, Hermann von, Axioms of Geometry, The, psychophysics 1153 1166 Helmholtz, Hermann von, Axioms of Geometry, The, sensations of tone 643 Helmholtz, Hermann von, Axioms of Geometry, The, space geometry 546 Helmholtz, Hermann von, Axioms of Geometry, The, space structure 645 647 681—682 696 Helmholtz, Hermann von, Axioms of Geometry, The, Theory of Animal Heat 643 Helmholtz, Hermann von, Axioms of Geometry, The, “On the Origin and Significance of Geometrical Axioms” 644 647—668 Hemibel thinking 2160—2161 Hemisphere, area of 175 Hempel, Carl G., biography 1615
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