Book Title: Shatkhandagama Pustak 04
Author(s): Pushpadant, Bhutbali, Hiralal Jain, Fulchandra Jain Shastri, Devkinandan, A N Upadhye
Publisher: Jain Sahityoddharak Fund Karyalay Amravati
View full book text
________________
(3) The logarithm ( ardhaccheda ) or the logarithm of & logarithm ( ardhaccheda-salaka ) was used to reduce the consideration of big numbers to those of smaller ones, e. g.
(i) Logg 2 = 2 (ii) Log, log, 44 = 3, (iii) Log, log, 256256 =
11.
It is no wonder to find that today we take recourse to one or the other of the above three methods of expressing numbers. The decimal place-value notation has become the common property of all nations. Logarithms are used whenever cal. culations with big numbers have to be made. Instances of the use of the law of indices to express magnitudes in modern physics is common. For instance, the number of protons in the Universe has been calculated and expressed as
136.2256
And Skewes' number which gives information regarding the distribution of primes is expressed in the form--
All the above methods of expressing numbers have been used in the Dhavală. It follows that the methods were commonly knowa before the seventh century A. D. in India.
........
1. The number 136. 2256 expressed in the decimal notation is 15,747,724,136,275,002,577 605,653,961,181,555.468,044,717,914, 572,116,709,366,231,425,076,185,631,031,296. It will be observed that the third vargita-samvargita of 2, i. e., 256256 is greater than the number of protons in the Universe. If we imagine the entire Universe as a chess-board, and the protons in it as chessmen, and if we agree to call any interchange in the position of two protons a' move' in this cosmic game, then the total number of possible moves would be the number -
84 10 10
10
This number is also connected with the theory of the distribution of primes.
Jain Education International
For Private & Personal Use Only
www.jainelibrary.org
Page Navigation
1 ... 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 ... 646