345
Index
Minamishinho village, 255 Minamoto shoguns, 13 missionaries, 4 Miyagi prefecture, 118 Miyake Chikataka, 164 Miyazaki prefecture, 150 Miyazawa Bunzaemon, 157 Mizuho sangaku, 111, 155 Mizuno Tsuneyuki, 100 modular arithmetic, 38–39 Momota, 253 monks, ix Morikawa Jihei, 265 Mo¯ri Shigeyoshi, 14–15, 31, 60–61, 64–65 movable type, 7 Mt. Asama, 247 Muramatsu Shigekiyo, 16, 65–66, 71 Murasaki, Shikibu, 13 Muromachi period, 13 music, 7, 30 Nagano prefecture, 96, 120, 159, 161, 247 Nagaoka city, 120, 252 Nagasaki, 4–5, 264 Nagata Takamichi, 102 Nagata Toshimasa, 100 Nagayoshi Nobuhiro, 116 Nagoaka Tenman shrine, 108 Nagoya, 100, 102, 198, 266 Nagoya Science Museum, xvii Naito¯ Masaki, 75 Nakamura Fumitora, 264 Nakamura Syuhei, 264 Nakamura Tokikazu, 118, 156, 168, 289, 296, 335–36 Nakane Genjun, 76–78 Nakane Genkei, 76 Nakashima Cho¯zaburo¯, 5 Nakasone Munekuni, 94 Nakata Ko¯kan, 148 Nara period, 10, 12–14, 256 Narazaki Hozuke, 261 Nature magazine, 288 negative numbers, 30 Neuberg, Jean Baptiste, 298–99 Neuberg’s theorem, 298–99 Newton, Isaac, 68, 73 Nezumi San (Mice Problem), 63 Niigata province, 244, 249 Niikappugun, 117 nine-point circle, 295–96 Nishihirokami Hachiman shrine, 148
Nishikannta shrine, 204 Nobuyoshi, 192 Noh drama, 7, 13 notation, xxv, 24 Notoyama Nobutomo, 155 Number Theory and Its History (Ore), 38n8, 163n3 Nunomura Jingoro¯, 256 Obama, 263 Oda Nobunaga, 14 Ogilvy, Stanley, 238n9 Ogura Yoshisada, 254, 263 Ohishi Manabu, 20n9 Ohita prefecture, 204 Ohma Shinmeisya shrine, 118 Ohsu Kannon temple, 100, 198 Ohta Sadaharu, 252 Okada Jiumon, 264 Okayama, 259 Okayu Yasumoto, 166, 208–9 Okazaki school, 81 Okuda Tsume, 106 Okuma, 247 105–subraction problem, 39 ¯ mura Kazuhide, 216, 236, 238, 288 O Ono Eiju¯, 199, 246n2, 247 On Tangencies (Apollonius), 284 “On the solutions to Malfatti’s problem for a triangle” (Lob and Richmond), 293n5 Opera Omnia Series Prima (Euler), 207 Ore, Oyestein, 38n8, 163n3 Osaka, 10, 14, 119, 254–55, 257 Owari clan, 82 Oyashirazu coast, 252 packing problems, 287–88 paper cutting, 76 Pascal, Blaise, 43 Pascal’s triangle, 42–46 Pedoe, Daniel, x–xi, xv–xvi, 296n8, 325n2 Perry, Matthew C., 3, 24 pi, 16, 19, 98, 188; Chinese and, 32, 40; Imamura and, 64; infinite series and, 75; integration and, 303–5; Isomura and, 66; Matsunaga and, 75; Muramatsu and, 65, 71; Seki and, 71–73, 75; Suanfa Tong Zong and, 42; Takebe and, 74–75 pilgrimages, 243–44 Pillow Book, The (Sei), 13
poetry, 7, 59, 64, 244 Pollock, Jackson, x Portuguese, 4–5 positive numbers, 30 power series, 304n2 primes, 80–81 printing, 7, 21 Ptolemy’s theorem, 283, 298 puppets, 7 Pythagoreans, 2 Pythagorean theorem, xxii, 83, 146, 283; cylinders and, 184; Descartes circle theorem and, 291; ellipses and, 240; fourth- order equations and, 223; inscribed circles and, 122–24, 129–30, 176, 179–80, 194, 214–15, inversion and, 321, 330–31, 334; Jiuzhang Suanshu and, 10, 28–29, 34–35; primitive triples and, 80–81, 284; quadratics and, 142–43, 241; similar triangles and, 172–73; Suanfa Tong Zong and, 50–52; Yamaguchi travel diary and, 277–79; Zenkoji temple sangaku and, 269–71 Qin Jiushao (Chin Chiu- Shao), 30 quadratics, xxii, 139; Descartes circle theorem (DCT) and, 228–31; ellipses and, 178–79; inscribed circles and, 170; Jiuzhang Suanshu and, 29; Pythagorean theorem and, 142–43, 241; reduction to quadratures and, 241; similar triangles and, 173 Record of the Ushikawa Inari Shrine Sangaku, 157 recreational mathematics, 76 reduction to quadratures, 241 reiyakukyutsu (dividing by zero), 85 religion: Buddhists, ix, xv, xviii, 2, 4, 9, 12–13, 265; chants, 13; Christians, 4–5; Jesuits, 4; missionaries and, 4; peace and, 12; pilgrimages and, 243–44; tolerance and, 12; Zen principles, 13 remainder theorem, 38 Renaissance, 7, 13, 69, 90 Richmond, H. W., 293–94 Rigby, J. F., 143, 189 Roku shrine, 246 Rothman, Tony, xii, xv–xviii Ruffini, Paolo, 40