 Golomb ruler of order 4 and length 6. This ruler is both optimal and perfect. In mathematics, a Golomb ruler, named after Solomon W. Golomb, is a set of marks at integer positions along an imaginary ruler such that no two pairs of marks are the same distance apart. The number of marks on the ruler is its order, and the largest distance between two of its marks is its length. Translation and reflection of a Golomb ruler are considered trivial, so the smallest mark is customarily put at 0 and the next mark at the smaller of its two possible values. The unique optimal Golomb ruler of order 4 (up to reflection and translation). ...
Wikibooks Wikiversity has more about this subject: School of Mathematics Wikiquote quotations related to: Mathematics Look up Mathematics in Wiktionary, the free dictionary Wikimedia Commons has more media related to: Mathematics Bogomolny, Alexander: Interactive Mathematics Miscellany and Puzzles. ...
Solomon W. Golomb Solomon Wolf Golomb (b. ...
A ruler is a person in charge of a country. ...
There is no requirement that a Golomb ruler can measure all distances up to its length, but if it does, it's called a perfect Golomb ruler. A Golomb ruler is optimal if no shorter Golomb ruler of the same order exists. Creating Golomb rulers is easy, but finding the optimal Golomb rulers for a specified order is computationally very challenging. Distributed.net has completed a distributed massively parallel search for optimal order-24 Golomb rulers, and a search for order-25 optimal rulers is currently underway. distributed. ...
Parallel computing is the simultaneous execution of the same task (split up and specially adapted) on multiple processors in order to obtain faster results. ...
One practical use of Golomb rulers is in the design of phased array radio antennae such as radio telescopes. Antennae in an [0,1,4,6] Golomb ruler configuration can often be seen at cell sites. A giant phased-array radar in Alaska In telecommunication, a phased array is a group of antennas in which the relative phases of the respective signals feeding the antennas are varied in such a way that the effective radiation pattern of the array is reinforced in a desired direction and...
The Parkes 64 metre radio telescope in New South Wales, Australia (the bigger of the two shown) In contrast to an ordinary telescope, which produces visible light images, a radio telescope sees radio waves emitted by radio sources, typically by means of a large parabolic (dish) antenna, or arrays of...
A cell site is a site where a wireless antenna and network communications equipment are placed for the use of mobile phones. ...
Known optimal Golomb rulers
The following table contains all known optimal Golomb rulers. The table is complete up to and including order 24. | order | length | marks | | 1 | 0 | 0 | | 2 | 1 | 0 1 | | 3 | 3 | 0 1 3 | | 4 | 6 | 0 1 4 6 | | 5 | 11 | 0 1 4 9 11
0 2 7 8 11 | | 6 | 17 | 0 1 4 10 12 17
0 1 4 10 15 17
0 1 8 11 13 17
0 1 8 12 14 17 | | 7 | 25 | 0 1 4 10 18 23 25
0 1 7 11 20 23 25
0 1 11 16 19 23 25
0 2 3 10 16 21 25
0 2 7 13 21 22 25 | | 8 | 34 | 0 1 4 9 15 22 32 34 | | 9 | 44 | 0 1 5 12 25 27 35 41 44 | | 10 | 55 | 0 1 6 10 23 26 34 41 53 55 | | 11 | 72 | 0 1 4 13 28 33 47 54 64 70 72
0 1 9 19 24 31 52 56 58 69 72 | | 12 | 85 | 0 2 6 24 29 40 43 55 68 75 76 85 | | 13 | 106 | 0 2 5 25 37 43 59 70 85 89 98 99 106 | | 14 | 127 | 0 4 6 20 35 52 59 77 78 86 89 99 122 127 | | 15 | 151 | 0 4 20 30 57 59 62 76 100 111 123 136 144 145 151 | | 16 | 177 | 0 1 4 11 26 32 56 68 76 115 117 134 150 163 168 177 | | 17 | 199 | 0 5 7 17 52 56 67 80 81 100 122 138 159 165 168 191 199 | | 18 | 216 | 0 2 10 22 53 56 82 83 89 98 130 148 153 167 188 192 205 216 | | 19 | 246 | 0 1 6 25 32 72 100 108 120 130 153 169 187 190 204 231 233 242 246 | | 20 | 283 | 0 1 8 11 68 77 94 116 121 156 158 179 194 208 212 228 240 253 259 283 | | 21 | 333 | 0 2 24 56 77 82 83 95 129 144 179 186 195 255 265 285 293 296 310 329 333 | | 22 | 356 | 0 1 9 14 43 70 106 122 124 128 159 179 204 223 253 263 270 291 330 341 353 356 | | 23 | 372 | 0 3 7 17 61 66 91 99 114 159 171 199 200 226 235 246 277 316 329 348 350 366 372 | | 24 | 425 | 0 9 33 37 38 97 122 129 140 142 152 191 205 208 252 278 286 326 332 353 368 384 403 425 | A search for optimal Golomb rulers of order 25 is currently underway (as of April 2005). It is predicted to be the following ruler, which was discovered in 1984 by M. D. Atkinson and A. Hassenklover. 1984 is a leap year starting on Sunday of the Gregorian calendar. ...
| order | length | marks | | 25 | 480 | 0 12 29 39 72 91 146 157 160 161 166 191 207 214 258 290 316 354 372 394 396 431 459 467 480 |
References - Martin Gardner, "Mathematical games", Scientific American, March 1972, p. 108-112
Martin Gardner (born October 21, 1914) is an American recreational mathematician, skeptic, and author of the long-running but now discontinued Mathematical Games column in Scientific American. ...
See also - Costas array
- Sparse ruler
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