Figures
4.1 “Tu on the Numerical Arrangement of the Yellow River Chart” (1743) 191
4.2 “Tu on the Numerical Arrangement of the Luo River Inscription” (1743) 191
4.3 “Tu on Confined Floods and Nine Sections” (1662) 195
4.4 “Tu on the Ruoshui in Ganzhou and Suzhou” (1181) 199
4.5 “Tu on the Sequence of the Qin Genealogy” (1662) 203
4.6 “Sequence of the Qin Genealogy” (1743) 203
4.7 “Tu on the Sequence of the Regulation of the Rivers” (1781) 205
4.8 “Tu on the System of the Five Domains under King Yao” (1662) 207
4.9 “Tu on the Five Duties Based on the Five Phases” (1673) 213
4.10 “Royal Perfection is Established in the Central Number Five of the Yellow River Chart and the Luo River Inscription” (1673) 215
4.11 General map on the “Tribute of Yu” (1827) 220
4.12 “Overview of the Nine Sections of the Great Plan” (1743) 222
5.1 A schematic representation of the recursive relation S <sub>i</sub> = 2 * S <sub>i–1</sub> + 1 246
5.2 “Diagrammatic Explanation of the Total Number of Sequential Combinations for Ten Objects” (1854) 247
5.3 “Diagrammatic Explanation of the Partial Number of Sequential Combinations for Ten Objects” (1854) 248
5.4 Illustration of C <sup>10</sup> <sub>1 </sub>= C <sup>10</sup> <sub>9 </sub>= 1 + 1 + 1 + … + 1 = 10 248
5.5 Illustration of C <sup>10</sup> <sub>2 </sub>= C <sup>10</sup> <sub>8 </sub>= 1 + 2 + … + 9 248
5.6 Illustration of C <sup>10</sup> <sub>3 </sub>= C <sup>10</sup> <sub>7 </sub>= 1 + 3 + 6 + 10 … + 36 249
5.7 Illustration of C <sup>10</sup> <sub>4 </sub>= C <sup>10</sup> <sub>6 </sub>= 1 + (1+3) + (1+3+6) + … + (1+3+6+10+15+21+28) 249
5.8 Inductive scheme applied by Wang Lai 252
5.9 The first ten lines of the Pascal Triangle (1867) 262
5.10 Unitary pebbles (1867) 263
11.1 “As you wish” wealth god (late 19th/early 20th-century) 496