Thursday, 24 April 2025

The Nautical Mile

Today I turned 27780 days old and one of the properties of this number is that it is a multiple of 1852:27780=15×1852The obvious question is so what? Well, 1852 turns out to be the length of a nautical mile in metres and numbers that are multiples of it belong to a special sequence, OEIS A303272. The initial members of the sequence are:

0, 1852, 3704, 5556, 7408, 9260, 11112, 12964, 14816, 16668, 18520, 20372, 22224, 24076, 25928, 27780, 29632, 31484, 33336, 35188, 37040, 38892, 40744, 42596, 44448, 46300, 48152, 50004, 51856, 53708, 55560, 57412, 59264, 61116, 62968, 64820, 66672, 68524


Figure 1

So if one day of my life represents a metre then I have today travelled 15 nautical miles on my journey through life. However, let's look more closely at how this figure of 1852 comes about. See Figure 1 and here are some excerpts from Wikipedia:

By the mid-19th century, France had defined a nautical mile via the original 1791 definition of the metre, one ten-millionth of a quarter meridian. So:10,000,00090×60=1,851.85 m 1,852 m became the metric length for a nautical mile. France made it legal for the French Navy in 1906, and many metric countries voted to sanction it for international use at the 1929 International Hydrographic Conference. In 1929 the international nautical mile was defined by the First International Extraordinary Hydrographic Conference in Monaco as exactly 1,852 metres (which is 6,076.12 ft). The United States did not adopt the international nautical mile until 1954. Britain adopted it in 1970. The derived unit of speed is the knot, one nautical mile per hour.

OEIS A303272 suggests a second similar sequence based on 1760, the number of yards in a mile. This would produce the follow initial members:

0, 1760, 3520, 5280, 7040, 8800, 10560, 12320, 14080, 15840, 17600, 19360, 21120, 22880, 24640, 26400, 28160, 29920, 31680, 33440, 35200, 36960, 38720, 40480, 42240, 44000, 45760, 47520, 49280, 51040, 52800, 54560, 56320, 58080, 59840, 61600, 63360, 65120, 66880, 68640, 70400

However, this sequence is not listed in the OEIS. Multiples of 5280, the number of feet in a mile, are included of course in the above sequence of numbers.

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