数学英語:to the nearest 45 degreesの意味

to the nearest 45 degreesの意味が全く分からんかったので調べてみることにした。

スポンサーリンク

Round to the nearest 45 degree

以下のコードは、thetaをto the nearest 45 degreesにroundする。

import numpy as np
for theta in range(0,361):
    a = np.floor((theta + 22.5) / 45) * 45
    print ("theta =",theta,"|","nearest 45 degree =", a)
theta = 0 | nearest 45 degree = 0.0
theta = 1 | nearest 45 degree = 0.0
theta = 2 | nearest 45 degree = 0.0
theta = 3 | nearest 45 degree = 0.0
theta = 4 | nearest 45 degree = 0.0
theta = 5 | nearest 45 degree = 0.0
theta = 6 | nearest 45 degree = 0.0
theta = 7 | nearest 45 degree = 0.0
theta = 8 | nearest 45 degree = 0.0
theta = 9 | nearest 45 degree = 0.0
theta = 10 | nearest 45 degree = 0.0
theta = 11 | nearest 45 degree = 0.0
theta = 12 | nearest 45 degree = 0.0
theta = 13 | nearest 45 degree = 0.0
theta = 14 | nearest 45 degree = 0.0
theta = 15 | nearest 45 degree = 0.0
theta = 16 | nearest 45 degree = 0.0
theta = 17 | nearest 45 degree = 0.0
theta = 18 | nearest 45 degree = 0.0
theta = 19 | nearest 45 degree = 0.0
theta = 20 | nearest 45 degree = 0.0
theta = 21 | nearest 45 degree = 0.0
theta = 22 | nearest 45 degree = 0.0
theta = 23 | nearest 45 degree = 45.0
theta = 24 | nearest 45 degree = 45.0
theta = 25 | nearest 45 degree = 45.0
theta = 26 | nearest 45 degree = 45.0
theta = 27 | nearest 45 degree = 45.0
theta = 28 | nearest 45 degree = 45.0
theta = 29 | nearest 45 degree = 45.0
theta = 30 | nearest 45 degree = 45.0
theta = 31 | nearest 45 degree = 45.0
theta = 32 | nearest 45 degree = 45.0
theta = 33 | nearest 45 degree = 45.0
theta = 34 | nearest 45 degree = 45.0
theta = 35 | nearest 45 degree = 45.0
theta = 36 | nearest 45 degree = 45.0
theta = 37 | nearest 45 degree = 45.0
theta = 38 | nearest 45 degree = 45.0
theta = 39 | nearest 45 degree = 45.0
theta = 40 | nearest 45 degree = 45.0
theta = 41 | nearest 45 degree = 45.0
theta = 42 | nearest 45 degree = 45.0
theta = 43 | nearest 45 degree = 45.0
theta = 44 | nearest 45 degree = 45.0
theta = 45 | nearest 45 degree = 45.0
theta = 46 | nearest 45 degree = 45.0
theta = 47 | nearest 45 degree = 45.0
theta = 48 | nearest 45 degree = 45.0
theta = 49 | nearest 45 degree = 45.0
theta = 50 | nearest 45 degree = 45.0
theta = 51 | nearest 45 degree = 45.0
theta = 52 | nearest 45 degree = 45.0
theta = 53 | nearest 45 degree = 45.0
theta = 54 | nearest 45 degree = 45.0
theta = 55 | nearest 45 degree = 45.0
theta = 56 | nearest 45 degree = 45.0
theta = 57 | nearest 45 degree = 45.0
theta = 58 | nearest 45 degree = 45.0
theta = 59 | nearest 45 degree = 45.0
theta = 60 | nearest 45 degree = 45.0
theta = 61 | nearest 45 degree = 45.0
theta = 62 | nearest 45 degree = 45.0
theta = 63 | nearest 45 degree = 45.0
theta = 64 | nearest 45 degree = 45.0
theta = 65 | nearest 45 degree = 45.0
theta = 66 | nearest 45 degree = 45.0
theta = 67 | nearest 45 degree = 45.0
theta = 68 | nearest 45 degree = 90.0
theta = 69 | nearest 45 degree = 90.0
theta = 70 | nearest 45 degree = 90.0
theta = 71 | nearest 45 degree = 90.0
theta = 72 | nearest 45 degree = 90.0
theta = 73 | nearest 45 degree = 90.0
theta = 74 | nearest 45 degree = 90.0
theta = 75 | nearest 45 degree = 90.0
theta = 76 | nearest 45 degree = 90.0
theta = 77 | nearest 45 degree = 90.0
theta = 78 | nearest 45 degree = 90.0
theta = 79 | nearest 45 degree = 90.0
theta = 80 | nearest 45 degree = 90.0
theta = 81 | nearest 45 degree = 90.0
theta = 82 | nearest 45 degree = 90.0
theta = 83 | nearest 45 degree = 90.0
theta = 84 | nearest 45 degree = 90.0
theta = 85 | nearest 45 degree = 90.0
theta = 86 | nearest 45 degree = 90.0
theta = 87 | nearest 45 degree = 90.0
theta = 88 | nearest 45 degree = 90.0
theta = 89 | nearest 45 degree = 90.0
theta = 90 | nearest 45 degree = 90.0
theta = 91 | nearest 45 degree = 90.0
theta = 92 | nearest 45 degree = 90.0
theta = 93 | nearest 45 degree = 90.0
theta = 94 | nearest 45 degree = 90.0
theta = 95 | nearest 45 degree = 90.0
theta = 96 | nearest 45 degree = 90.0
theta = 97 | nearest 45 degree = 90.0
theta = 98 | nearest 45 degree = 90.0
theta = 99 | nearest 45 degree = 90.0
theta = 100 | nearest 45 degree = 90.0
theta = 101 | nearest 45 degree = 90.0
theta = 102 | nearest 45 degree = 90.0
theta = 103 | nearest 45 degree = 90.0
theta = 104 | nearest 45 degree = 90.0
theta = 105 | nearest 45 degree = 90.0
theta = 106 | nearest 45 degree = 90.0
theta = 107 | nearest 45 degree = 90.0
theta = 108 | nearest 45 degree = 90.0
theta = 109 | nearest 45 degree = 90.0
theta = 110 | nearest 45 degree = 90.0
theta = 111 | nearest 45 degree = 90.0
theta = 112 | nearest 45 degree = 90.0
theta = 113 | nearest 45 degree = 135.0
theta = 114 | nearest 45 degree = 135.0
theta = 115 | nearest 45 degree = 135.0
theta = 116 | nearest 45 degree = 135.0
theta = 117 | nearest 45 degree = 135.0
theta = 118 | nearest 45 degree = 135.0
theta = 119 | nearest 45 degree = 135.0
theta = 120 | nearest 45 degree = 135.0
theta = 121 | nearest 45 degree = 135.0
theta = 122 | nearest 45 degree = 135.0
theta = 123 | nearest 45 degree = 135.0
theta = 124 | nearest 45 degree = 135.0
theta = 125 | nearest 45 degree = 135.0
theta = 126 | nearest 45 degree = 135.0
theta = 127 | nearest 45 degree = 135.0
theta = 128 | nearest 45 degree = 135.0
theta = 129 | nearest 45 degree = 135.0
theta = 130 | nearest 45 degree = 135.0
theta = 131 | nearest 45 degree = 135.0
theta = 132 | nearest 45 degree = 135.0
theta = 133 | nearest 45 degree = 135.0
theta = 134 | nearest 45 degree = 135.0
theta = 135 | nearest 45 degree = 135.0
theta = 136 | nearest 45 degree = 135.0
theta = 137 | nearest 45 degree = 135.0
theta = 138 | nearest 45 degree = 135.0
theta = 139 | nearest 45 degree = 135.0
theta = 140 | nearest 45 degree = 135.0
theta = 141 | nearest 45 degree = 135.0
theta = 142 | nearest 45 degree = 135.0
theta = 143 | nearest 45 degree = 135.0
theta = 144 | nearest 45 degree = 135.0
theta = 145 | nearest 45 degree = 135.0
theta = 146 | nearest 45 degree = 135.0
theta = 147 | nearest 45 degree = 135.0
theta = 148 | nearest 45 degree = 135.0
theta = 149 | nearest 45 degree = 135.0
theta = 150 | nearest 45 degree = 135.0
theta = 151 | nearest 45 degree = 135.0
theta = 152 | nearest 45 degree = 135.0
theta = 153 | nearest 45 degree = 135.0
theta = 154 | nearest 45 degree = 135.0
theta = 155 | nearest 45 degree = 135.0
theta = 156 | nearest 45 degree = 135.0
theta = 157 | nearest 45 degree = 135.0
theta = 158 | nearest 45 degree = 180.0
theta = 159 | nearest 45 degree = 180.0
theta = 160 | nearest 45 degree = 180.0
theta = 161 | nearest 45 degree = 180.0
theta = 162 | nearest 45 degree = 180.0
theta = 163 | nearest 45 degree = 180.0
theta = 164 | nearest 45 degree = 180.0
theta = 165 | nearest 45 degree = 180.0
theta = 166 | nearest 45 degree = 180.0
theta = 167 | nearest 45 degree = 180.0
theta = 168 | nearest 45 degree = 180.0
theta = 169 | nearest 45 degree = 180.0
theta = 170 | nearest 45 degree = 180.0
theta = 171 | nearest 45 degree = 180.0
theta = 172 | nearest 45 degree = 180.0
theta = 173 | nearest 45 degree = 180.0
theta = 174 | nearest 45 degree = 180.0
theta = 175 | nearest 45 degree = 180.0
theta = 176 | nearest 45 degree = 180.0
theta = 177 | nearest 45 degree = 180.0
theta = 178 | nearest 45 degree = 180.0
theta = 179 | nearest 45 degree = 180.0
theta = 180 | nearest 45 degree = 180.0
theta = 181 | nearest 45 degree = 180.0
theta = 182 | nearest 45 degree = 180.0
theta = 183 | nearest 45 degree = 180.0
theta = 184 | nearest 45 degree = 180.0
theta = 185 | nearest 45 degree = 180.0
theta = 186 | nearest 45 degree = 180.0
theta = 187 | nearest 45 degree = 180.0
theta = 188 | nearest 45 degree = 180.0
theta = 189 | nearest 45 degree = 180.0
theta = 190 | nearest 45 degree = 180.0
theta = 191 | nearest 45 degree = 180.0
theta = 192 | nearest 45 degree = 180.0
theta = 193 | nearest 45 degree = 180.0
theta = 194 | nearest 45 degree = 180.0
theta = 195 | nearest 45 degree = 180.0
theta = 196 | nearest 45 degree = 180.0
theta = 197 | nearest 45 degree = 180.0
theta = 198 | nearest 45 degree = 180.0
theta = 199 | nearest 45 degree = 180.0
theta = 200 | nearest 45 degree = 180.0
theta = 201 | nearest 45 degree = 180.0
theta = 202 | nearest 45 degree = 180.0
theta = 203 | nearest 45 degree = 225.0
theta = 204 | nearest 45 degree = 225.0
theta = 205 | nearest 45 degree = 225.0
theta = 206 | nearest 45 degree = 225.0
theta = 207 | nearest 45 degree = 225.0
theta = 208 | nearest 45 degree = 225.0
theta = 209 | nearest 45 degree = 225.0
theta = 210 | nearest 45 degree = 225.0
theta = 211 | nearest 45 degree = 225.0
theta = 212 | nearest 45 degree = 225.0
theta = 213 | nearest 45 degree = 225.0
theta = 214 | nearest 45 degree = 225.0
theta = 215 | nearest 45 degree = 225.0
theta = 216 | nearest 45 degree = 225.0
theta = 217 | nearest 45 degree = 225.0
theta = 218 | nearest 45 degree = 225.0
theta = 219 | nearest 45 degree = 225.0
theta = 220 | nearest 45 degree = 225.0
theta = 221 | nearest 45 degree = 225.0
theta = 222 | nearest 45 degree = 225.0
theta = 223 | nearest 45 degree = 225.0
theta = 224 | nearest 45 degree = 225.0
theta = 225 | nearest 45 degree = 225.0
theta = 226 | nearest 45 degree = 225.0
theta = 227 | nearest 45 degree = 225.0
theta = 228 | nearest 45 degree = 225.0
theta = 229 | nearest 45 degree = 225.0
theta = 230 | nearest 45 degree = 225.0
theta = 231 | nearest 45 degree = 225.0
theta = 232 | nearest 45 degree = 225.0
theta = 233 | nearest 45 degree = 225.0
theta = 234 | nearest 45 degree = 225.0
theta = 235 | nearest 45 degree = 225.0
theta = 236 | nearest 45 degree = 225.0
theta = 237 | nearest 45 degree = 225.0
theta = 238 | nearest 45 degree = 225.0
theta = 239 | nearest 45 degree = 225.0
theta = 240 | nearest 45 degree = 225.0
theta = 241 | nearest 45 degree = 225.0
theta = 242 | nearest 45 degree = 225.0
theta = 243 | nearest 45 degree = 225.0
theta = 244 | nearest 45 degree = 225.0
theta = 245 | nearest 45 degree = 225.0
theta = 246 | nearest 45 degree = 225.0
theta = 247 | nearest 45 degree = 225.0
theta = 248 | nearest 45 degree = 270.0
theta = 249 | nearest 45 degree = 270.0
theta = 250 | nearest 45 degree = 270.0
theta = 251 | nearest 45 degree = 270.0
theta = 252 | nearest 45 degree = 270.0
theta = 253 | nearest 45 degree = 270.0
theta = 254 | nearest 45 degree = 270.0
theta = 255 | nearest 45 degree = 270.0
theta = 256 | nearest 45 degree = 270.0
theta = 257 | nearest 45 degree = 270.0
theta = 258 | nearest 45 degree = 270.0
theta = 259 | nearest 45 degree = 270.0
theta = 260 | nearest 45 degree = 270.0
theta = 261 | nearest 45 degree = 270.0
theta = 262 | nearest 45 degree = 270.0
theta = 263 | nearest 45 degree = 270.0
theta = 264 | nearest 45 degree = 270.0
theta = 265 | nearest 45 degree = 270.0
theta = 266 | nearest 45 degree = 270.0
theta = 267 | nearest 45 degree = 270.0
theta = 268 | nearest 45 degree = 270.0
theta = 269 | nearest 45 degree = 270.0
theta = 270 | nearest 45 degree = 270.0
theta = 271 | nearest 45 degree = 270.0
theta = 272 | nearest 45 degree = 270.0
theta = 273 | nearest 45 degree = 270.0
theta = 274 | nearest 45 degree = 270.0
theta = 275 | nearest 45 degree = 270.0
theta = 276 | nearest 45 degree = 270.0
theta = 277 | nearest 45 degree = 270.0
theta = 278 | nearest 45 degree = 270.0
theta = 279 | nearest 45 degree = 270.0
theta = 280 | nearest 45 degree = 270.0
theta = 281 | nearest 45 degree = 270.0
theta = 282 | nearest 45 degree = 270.0
theta = 283 | nearest 45 degree = 270.0
theta = 284 | nearest 45 degree = 270.0
theta = 285 | nearest 45 degree = 270.0
theta = 286 | nearest 45 degree = 270.0
theta = 287 | nearest 45 degree = 270.0
theta = 288 | nearest 45 degree = 270.0
theta = 289 | nearest 45 degree = 270.0
theta = 290 | nearest 45 degree = 270.0
theta = 291 | nearest 45 degree = 270.0
theta = 292 | nearest 45 degree = 270.0
theta = 293 | nearest 45 degree = 315.0
theta = 294 | nearest 45 degree = 315.0
theta = 295 | nearest 45 degree = 315.0
theta = 296 | nearest 45 degree = 315.0
theta = 297 | nearest 45 degree = 315.0
theta = 298 | nearest 45 degree = 315.0
theta = 299 | nearest 45 degree = 315.0
theta = 300 | nearest 45 degree = 315.0
theta = 301 | nearest 45 degree = 315.0
theta = 302 | nearest 45 degree = 315.0
theta = 303 | nearest 45 degree = 315.0
theta = 304 | nearest 45 degree = 315.0
theta = 305 | nearest 45 degree = 315.0
theta = 306 | nearest 45 degree = 315.0
theta = 307 | nearest 45 degree = 315.0
theta = 308 | nearest 45 degree = 315.0
theta = 309 | nearest 45 degree = 315.0
theta = 310 | nearest 45 degree = 315.0
theta = 311 | nearest 45 degree = 315.0
theta = 312 | nearest 45 degree = 315.0
theta = 313 | nearest 45 degree = 315.0
theta = 314 | nearest 45 degree = 315.0
theta = 315 | nearest 45 degree = 315.0
theta = 316 | nearest 45 degree = 315.0
theta = 317 | nearest 45 degree = 315.0
theta = 318 | nearest 45 degree = 315.0
theta = 319 | nearest 45 degree = 315.0
theta = 320 | nearest 45 degree = 315.0
theta = 321 | nearest 45 degree = 315.0
theta = 322 | nearest 45 degree = 315.0
theta = 323 | nearest 45 degree = 315.0
theta = 324 | nearest 45 degree = 315.0
theta = 325 | nearest 45 degree = 315.0
theta = 326 | nearest 45 degree = 315.0
theta = 327 | nearest 45 degree = 315.0
theta = 328 | nearest 45 degree = 315.0
theta = 329 | nearest 45 degree = 315.0
theta = 330 | nearest 45 degree = 315.0
theta = 331 | nearest 45 degree = 315.0
theta = 332 | nearest 45 degree = 315.0
theta = 333 | nearest 45 degree = 315.0
theta = 334 | nearest 45 degree = 315.0
theta = 335 | nearest 45 degree = 315.0
theta = 336 | nearest 45 degree = 315.0
theta = 337 | nearest 45 degree = 315.0
theta = 338 | nearest 45 degree = 360.0
theta = 339 | nearest 45 degree = 360.0
theta = 340 | nearest 45 degree = 360.0
theta = 341 | nearest 45 degree = 360.0
theta = 342 | nearest 45 degree = 360.0
theta = 343 | nearest 45 degree = 360.0
theta = 344 | nearest 45 degree = 360.0
theta = 345 | nearest 45 degree = 360.0
theta = 346 | nearest 45 degree = 360.0
theta = 347 | nearest 45 degree = 360.0
theta = 348 | nearest 45 degree = 360.0
theta = 349 | nearest 45 degree = 360.0
theta = 350 | nearest 45 degree = 360.0
theta = 351 | nearest 45 degree = 360.0
theta = 352 | nearest 45 degree = 360.0
theta = 353 | nearest 45 degree = 360.0
theta = 354 | nearest 45 degree = 360.0
theta = 355 | nearest 45 degree = 360.0
theta = 356 | nearest 45 degree = 360.0
theta = 357 | nearest 45 degree = 360.0
theta = 358 | nearest 45 degree = 360.0
theta = 359 | nearest 45 degree = 360.0
theta = 360 | nearest 45 degree = 360.0

to the nearest 45 degreeの意味

上のコードの実行結果によると、例えば、θが67だとnearest 45 degreeは45で、θが68だと90になることから、to the nearest 45 degreesの意味は、最寄りの45度、もしくは、直近の45度、あるいは、最短の45度という意味になると思われる。なので、Round the A to the nearest 45 degrees.なら、Aを直近の45度へ四捨五入せよと訳せる。45 degreesが複数形なのは、0度、45度、90度、135度、180度、225度、270度、315度、360度等を含むためだと思われる。