5040 and 7920
▪ As previously stated, 5040 is the product of both 1 × 2 × 3 × 4 × 5 × 6 × 7 and 7 × 8 × 9 × 10. Additionally, 7920 is the product of 8 × 9 × 10 × 11.
▪ The ratio 7920/5040, which is (11!/7!)/7!, or equivalently 11!/(7!)², also equals 11/7. The numbers 11 and 7 are the only other pair of natural numbers (along with 3 and 2) for which this occurs: (n!/m!)/m! = n/m; or equivalently: n!/(m!)² = n/m.
▪ The ratio 7920/5040 simplifies to 11/7, which is π/2 (when using 22/7 for π). Similarly, 5040/7920 is 7/11, which is 2/π (when using 22/7 for π).
▪ Given a circle with radius 5040 units, a quarter of that circle's circumference is 7920 units (when using 22/7 for π).
▪ On the 27th of August, 2002, a crop formation was discovered at Crooked Soley in Wiltshire, England that had an outer ring split into 1,296 curved, diamond-like sections. The crops in 504 of those sections were still standing while the crops in the other 792 were leaning virtually horizontally.
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