The Cult of Pythagoras: Math and Myths

Index

259 INDEX Abel, Niels Henrik, 66 Aczel, Amir, 90 Agalophamus, 17 aleph, 192 Alexander, Amir, 22, 23, 56 algebra, 87–88, 92, 110–12, 133, 186–90; and computers, 90; conventions in, 86, 109–12, 184–85; and Euler, 83–84, 100, 102–10; and Hamilton, 116–21, 205; as independent of analogies, 183; as the Science of Pure Time, 111, 116; of vectors, 128–30, 200 Anaxagoras, 58 Anderson, James, 90–93, 96–99, 235n15 Anticlides, 12, 220n47 Apollo, 2, 3–4, 6–7, 203 Apollodorus, 4–5, 11, 219 Apollonius of Perga, 8, 43, 220, 221n50 Archimedes: death of, 53–58; on equilibrium, 46; on Euclid, 220n38, 226nn1–2; on geometry, 43, 45–48; on infinitesimals, 146, 153; and king Hiero’s crown, 48–51; on the mechanical method, 46–47; mentioned, 8, 205; and the siege of Syracuse, 51–54 architecture, xvii, 5–6, 75–78, 191, 200, 206–7 Archytas, 38 Argand, Jean Robert, 94 Aristotle, 7, 24–26, 65, 204, 205; on division by zero, 82, 85; in hearsay or misrepresented, 35, 219n32, 221n50; on incommensurables, 25; on the sciences, 39; on the Pythagoreans, 8, 10, 16–17, 35, 209 Aristophanes, 223n18 Aristoxenus, 7, 10, 13, 205 arithmetic, 204; as absolute reality, 40, 185, 191; Aristotle on, 39; and baseball, 89; and computers, 90–92, 97–99; as natural, 185; Plato on, 33–35, 146; and Pythagoras, 10, 207; and religious enlightenment, 33, 35, 40–41; rules of, 89, 111–12, 155; as timeless, 185; and triplets, 115 associative rule, 125, 129, 132, 188 Athenaeus, xv, 5, 11 Austin, J. L., 182 Babylonians, 1, 9 Baez, John C., 132 Barthélemy, Jean-Jacques, 212 Beckmann, Petr, 56 Beethoven, Ludwig van, 211 260 I N D E X Bell, Eric Temple, 10, 56, 60–62, 132 Beltrami, Eugenio, 172 Berkeley, George, 146–48, 153, 181 Bernoulli, Johann, 103, 145 Bézout, Etienne, 105–7, 110–11 Bhaskara, 82, 85 Bible, 146, 170, 196, 207, 253nn37–38 Bishop, Errett, 198 Blavatsky, Helena, 210 Bolyai, Farkas, 160–61, 172 Bolyai, János, 160–61, 169–72, 185, 246n28 Boyer, Carl, 145, 151 Brahmagupta, 82, 85 Brahe, Tycho, 177 Brower, L. E. J., 198 Brown, Dan, 79–80 Bruno, Giordano, 145, 177 Buddha, 206, 214 Burkert, Walter, 14, 202 Burnet, John, 21, 23 Butler, William Archer, 126 Byrne, Rhonda, xvii, 211 Cajori, Florian, 104, 108 calculus, 97, 132, 139–53 Callimachus, 12 Cantor, Georg, xviii, 150–51, 153, 191–94, 198, 249n9 Cardano, Girolamo, 87 Cauchy, Augustin Louis, 63–64, 148–50, 153 Cayley, Arthur, 125, 131 Cervantes, Miguel, 65 Cesi, Federico, 248n49 Choike, James R., 23 Cicero, Marcus Tullius, 6–8, 11, 43, 54–58, 148, 213 circle, 158; and Archimedes, 54, 56, 227n23; of numbers, 93–94; reality of, xx–xxi, 115, 175, 177–80, 196–97; and Riemann, 171–72; squaring the, 47, 67, 151, 169 commutative rule, 112, 118, 123, 125, 184, 187–88, 192 complex numbers, 94, 104–5, 113–14, 117–19, 132, 186, 190 constructivism, 198 Copernicus, Nicolaus, 175, 177 Courant, Richard, 91, 93 Couturat, Louis, 85 Crease, Robert, xix, xxi, 8, 220n35 d’Alembert, Jean, 87–88, 103, 160 Dauben, Joseph, 193 Da Vinci, Leonardo, 78–80, 211 Davis, Philip, 41, 151, 198–99, 244n36 Day, Jeremiah, 106 Dee, John, 39–40 de Foncenex, François, 103 Degen, C. F., 239n16 de Jonge, Marinus, 208, 253n38 De Morgan, Augustus, 85, 96, 125 Democritus, 58 Derbyshire, John, 19, 23 Descartes, René, 158 Diodorus of Sicily, 7, 10, 12 Diogenes, See Laertius, Diogenes Disney, Walt, xviii, 77–78, 81 Dositheus, 47 Dresden, Arnold, 131 du Bois-Reymond, Paul, 153 Dumotel, Stéphanie, 67–68, 70 Dyson, Frank, 247n36 Eco, Umberto, 16 Eddington, Arthur Stanley, 247n36 Einstein, 2, 156, 173, 174–76, 208, 211, 247n36 Elements, The (Euclid), 43–45; commentaries on, 15, 21, 39; contents of 26, 38, 44–45, 70, 146, 158–60, 165–66, 171; date of 8–9, 220n38; mentioned, 25, 103, 159. See also Euclid Emch, Arnold, 93 Empedocles, 8 Eratosthenes, 47 Euclid, 43–44, 205; and The Elements, 8, 26, 43–44, 103, 148, 158, 165–77, 180, 189; on infinitesimals, 243n22; on motion, 44; and the regular solids, 26, 44; on parallel lines, 158–62; and the Pythagorean theorem, 9; when he lived, 220n38, 226n1 Eudemus, 3 Eudoxus, 7, 38 I N D E X 261 Euler, Leonhard, 84, 103–8; on division...