Europe Data set:> eurodist Athens Barcelona…

Human Mathematics

12 years ago

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Europe

Data set:
> eurodist Athens Barcelona Brussels Calais Cherbourg Cologne Copenhagen Barcelona 3313 Brussels 2963 1318 Calais 3175 1326 204 Cherbourg 3339 1294 583 460 Cologne 2762 1498 206 409 785 Copenhagen 3276 2218 966 1136 1545 760 Geneva 2610 803 677 747 853 1662 1418 Gibraltar 4485 1172 2256 2224 2047 2436 3196 Hamburg 2977 2018 597 714 1115 460 460 Hook of Holland 3030 1490 172 330 731 269 269 Lisbon 4532 1305 2084 2052 1827 2290 2971 Lyons 2753 645 690 739 789 714 1458 Madrid 3949 636 1558 1550 1347 1764 2498 Marseilles 2865 521 1011 1059 1101 1035 1778 Milan 2282 1014 925 1077 1209 911 1537 Munich 2179 1365 747 977 1160 583 1104 Paris 3000 1033 285 280 340 465 1176 Rome 817 1460 1511 1662 1794 1497 2050 Stockholm 3927 2868 1616 1786 2196 1403 650 Vienna 1991 1802 1175 1381 1588 937 1455 Geneva Gibraltar Hamburg Hook of Holland Lisbon Lyons Madrid Barcelona Brussels Calais Cherbourg Cologne Copenhagen Geneva Gibraltar 1975 Hamburg 1118 2897 Hook of Holland 895 2428 550 Lisbon 1936 676 2671 2280 Lyons 158 1817 1159 863 1178 Madrid 1439 698 2198 1730 668 1281 Marseilles 425 1693 1479 1183 1762 320 1157 Milan 328 2185 1238 1098 2250 328 1724 Munich 591 2565 805 851 2507 724 2010 Paris 513 1971 877 457 1799 471 1273 Rome 995 2631 1751 1683 2700 1048 2097 Stockholm 2068 3886 949 1500 3231 2108 3188 Vienna 1019 2974 1155 1205 2937 1157 2409 Marseilles Milan Munich Paris Rome Stockholm Barcelona Brussels Calais Cherbourg Cologne Copenhagen Geneva Gibraltar Hamburg Hook of Holland Lisbon Lyons Madrid Marseilles Milan 618 Munich 1109 331 Paris 792 856 821 Rome 1011 586 946 1476 Stockholm 2428 2187 1754 1827 2707 Vienna 1363 898 428 1249 1209 2105

Multi-dimensional scaling of the distances:

> cmdscale(eurodist) [,1] [,2] Athens 2290.274680 1798.80293 Barcelona -825.382790 546.81148 Brussels 59.183341 -367.08135 Calais -82.845973 -429.91466 Cherbourg -352.499435 -290.90843 Cologne 293.689633 -405.31194 Copenhagen 681.931545 -1108.64478 Geneva -9.423364 240.40600 Gibraltar -2048.449113 642.45854 Hamburg 561.108970 -773.36929 Hook of Holland 164.921799 -549.36704 Lisbon -1935.040811 49.12514 Lyons -226.423236 187.08779 Madrid -1423.353697 305.87513 Marseilles -299.498710 388.80726 Milan 260.878046 416.67381 Munich 587.675679 81.18224 Paris -156.836257 -211.13911 Rome 709.413282 1109.36665 Stockholm 839.445911 -1836.79055 Vienna 911.230500 205.93020

Plot

require(stats) loc <- cmdscale(eurodist) rx <- range(x <- loc[,1]) ry <- range(y <- -loc[,2]) plot(x, y, type="n", asp=1, xlab="", ylab="") abline(h = pretty(rx, 10), v = pretty(ry, 10), col = "light gray") text(x, y, labels(eurodist), cex=0.8)

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