User talk:Paul Martin/Hexadecimal metric system/Archive 02

Also see: SMH talk: Archive I and Hexadecimal metric system.

The new digital foot
The hexadecimal foot compared to the Roman foot, Austrian foot (i.e. the Greek "pous metrios") and to the English and French foot measures :

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 * colspan=5 height=48| Comparison distances  (all below values in millimetres)
 * bgcolor=#F0F0F0 height=|
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 * 1575 x 9 / 0.27706     ≥  511 622.031
 * 1620 x 1896.5 / 6             =           512 055
 * 1680 x 304.8                  =           512 064
 * 1715 x 19 109.257 / 64        =           512 068.371 171 875
 * 1728 x 296.352                =           512 096.256


 * - bgcolor=#F0F0F0
 * width=  | Ratio
 * width= 72| Foot
 * width=120| French     definition (1799)
 * width=120| Austrian   definition (1872)
 * width=120| Anglo-saxon definition (1959)
 * width=240| Scientific definition (1990)
 * width=120| Idealistic definition (2003)


 * height=28 width=48| 1575
 * bgcolor=#FCFCFC| French
 * ≤ 324.839 385
 * ≤ 325.114 286
 * = 325.120 000
 * = 325.122 775 347 222 222 222 222
 * = 325.140 480
 * = 325.140 480


 * height=28 width=48| 1620
 * bgcolor=#FCFCFC| Austrian
 * ≤ 315.816 069
 * = 316.08 3  333
 * = 316.0 88 888
 * = 316.091 587 143 132 716 049 382
 * = 316.108 800
 * = 316.108 800


 * height=28 width=48| 1680
 * bgcolor=#FCFCFC| English
 * ≥ 304.536 923
 * ≤ 304.794 643
 * = 304.8 00 000
 * = 304.802 601 888 020 8 33 333 333
 * = 304.819 200
 * = 304.819 200


 * height=28| 1715
 * bgcolor=#FCFCFC| Digital
 * ≥ 298.321 884
 * ≥ 298.574 344
 * ≤ 298.579 592
 * = 298.582 140 625 000 000 000 000
 * = 298.598 400
 * = 298.598 400


 * height=28| 1728
 * bgcolor=#FCFCFC | Roman
 * ≥ 296.077 564
 * = 296.328 125
 * = 296. 333 333
 * = 296.335 862 946 686 921 296 296
 * = 296.352 000
 * bgcolor=#F0F0F0 height=28 colspan=2| Percentages :
 * ≤  99.912 836 %
 * ≤  99.997 389 %
 * ≥  99.999 146 %
 * =     100.000 000 000 %
 * ≥ 100.005 445 %
 * =     100.000 000 000 %
 * ≥ 100.005 445 %


 * colspan=7 bgcolor=#F0F0F0 height=|
 * }
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Ratios between these five foot measures, notably their linear relationship to the new digital foot.

The exact value of the scientific 64-foot-chain is by its definition of 1990: 19 109 257 micrometres. This value is a huge prime number. Therefore, the scientific and idealistic values entertain the ratio: (19 109 257 x 10)  :  (1728 x 1728 x 64),  a factor of  ≈ 0.999 945 5.