"DMT-EDMT Series for December Geometry #24"
acrylic, 17"x14", 2023, Reginald Brooks
A TRUE Mp-PN pairing:
The Center in ORANGE -- first doubling, that of the Butterfly Fractal 1 (BF1): 1--2--4--8--16, p=5 entries culminating with x=16, while y= 1+2+4+8=15. Together they sum to 31=z=Mp.
The Center above (Lt.gray) -- second doubling, that of the BF1 x 31: 31--62--124--248--496,,2p=10 total entries culminating with xz=Perfect Number (PN)=496.
31+62+124+248=yz=ODD Complement (OC) =465. Together, PN+OC=496+465=Mersenne Prime Square (MPS)=z² =Mp² = 961.
Take away all the labeling ornamentation and you are left with the barebones entries of 5 each:
1st Doubling: 1---2-----4-----8---16
2nd Doubling: 31--62--124--248--496
These, two lines are straight out of the Divisor Matrix Table (DMT) at Row 1 and Row31, respectively.
And, as 496 divides sequentially down to 31 and 31 is Prime, these 10 numbers are the divisors of 496. The first 9 = factors (proper divisors) of 496 and ∑ = 496 = PN.
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Cheers!
