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the regular expansion rate of a square
POSTULATE 1.1: re. the Even expansion rate of 4^2
AXIOM 1.2: consider the Unit square as 1^2, and the
square of the unit sqaure as 2^2 in planar 2-space.
LEMMA 1.3: the Unit square in 2-space is 1X1 with a
diaganol “root” =!2.
THEOREM 1.4: the Unit square squared in 2-space is =
2^2, or the Area-4 square.
AXIOM 1.5: consider the square of the Unit square as
= 2^2; thus the cube of the Unit square in 2-space is =
to 2^3 = 8 in volume, & in 2-space = 4 in Area.
LEMMA 1.6: thus in 3-space, the Unit square cubed =
the same as the 4-square in 2-space.
THEOREM 1.7: the Unit square cubed in 3-space =
the Area-4 square in 2-space.
AXIOM 1.8: expansion in 2-space measures the shadow
of expansion in 3-space.