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▪ 5040 is considered an important number in some systems of numerology, not only because of the Plato connection, but because using round figures, the sum of the radii of both the Earth and Moon (in miles) is 3960 + 1080 = 5040. Incidentally, the sum of their diameters is also the number of minutes in a week (7 days × 24 hours × 60 minutes = 10,080).
▪ The ratio of the radius of the moon and the radius of the earth is 1080/3960, which simplifies to 3/11. This ratio can also be expressed as (4 - π)/π, when using 22/7 as the value of π. This means that the sizes of the earth and the moon are related by a simple function of π.
▪ Given that the radius of the moon is 3/11 that of the earth, the sum of their radii can be broken into 3/14 (for the radius of the moon) and 11/14 (for the radius of the earth). Further, the sum of their radii in miles is 5040, which when divided by 14 is 360 (the number of degrees in a circle). This would not happen for another pair of objects with radii in the same ratio - it only happens when the sum of their radii is 5040.
▪ 5040 has exactly 60 divisors, counting itself and 1.
▪ In a vigesimal system, 5040 is represented as 12 groups of 20's and 12 groups of 20-squared's (12 • 20 = 240, 12 • 202 = 4800, and 240 + 4800 = 5040).
▪ 5040 is the sum of 42 consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101 + 103 + 107 + 109 + 113 + 127 + 131 + 137 + 139 + 149 + 151 + 157 +163 + 167 + 173 + 179 + 181 + 191 + 193 + 197 + 199 + 211 + 223 + 227 + 229).
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