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Shower Thoughts: Maths
Jul. 13th, 2025 06:15 pmSo... we were watching an 8-player Round Robin Starcraft competition yesterday, and noticed that (8)C(2) [the number of matches] is 28, which happens to be a Perfect Number -- so I wondered if it was coincidence.
Today, while I was in the shower, I did a big of calculation...
Friends, It is NOT a coincidence at all!
(2^p)C(2) = {(2^p) * [(2^p)-1]}/2
Which = [(2^p)/2] * [(2^p) - 1]
Which = [2^(p-1)] * [(2^p)-1]
...which is the form of all even Perfect Numbers!!!
(That second term is a Mersenne Number, and when it is prime, it's a Mersenne Prime -- and the complete expression is a Perfect Number)
Today, while I was in the shower, I did a big of calculation...
Friends, It is NOT a coincidence at all!
(2^p)C(2) = {(2^p) * [(2^p)-1]}/2
Which = [(2^p)/2] * [(2^p) - 1]
Which = [2^(p-1)] * [(2^p)-1]
...which is the form of all even Perfect Numbers!!!
(That second term is a Mersenne Number, and when it is prime, it's a Mersenne Prime -- and the complete expression is a Perfect Number)
