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If a line — and broken line – – are represented by the algebraic symbols "a" and "b" and
non-commutivity of their multiplication is assumed, i.e., ab ≠ ba, the eight trigrams express the eight possible
terms in the cubic expansion of (a+b)^{3}. The **64** hexagrams express the
**64** possible terms in the expansion of (a+b)^{6} =
(a+b)^{3}×(a+b)^{3}. The conclusion of the analysis presented here does not depend on assuming
non-commutivity, so let us drop this assumption for convenience. The eight diagonal hexagrams symbolize the eight
terms in the expansion of (a^{2}+b^{2})^{3}. Terms that correspond to off-diagonal
hexagrams that contain even powers of a and b are written in red; their counterpart hexagrams are likewise
coloured. Terms with odd powers of a and b are written in blue; they correspond to blue off-diagonal hexagrams. In
each off-diagonal half of the I Ching table, there are three blue hexagrams symbolizing the term a^{5}b,
six red hexagrams symbolizing the term a^{4}b^{2}, 10 blue hexgarams symbolizing the term
a^{3}b^{3}, six red hexagrams symbolizing the term a^{2}b^{4} and three blue
hexagrams symbolizing the term ab^{5}. The **168** lines & broken lines comprise 78
lines & broken lines that symbolize the terms a^{5}b and a^{3}b^{3} and 90 lines
& broken lines that symbolize the terms a^{4}b^{2}, a^{2}b^{4} &
ab^{5}. There is ambiguity here whether the term a^{5}b or ab^{5} is to be associated
with the 78 lines & broken lines because each corresponds to 18 lines & broken lines. This means that
there are two possible ways of identifying the sets of 78 and 90 lines & broken lines. But which one is correct
does not matter as far as the conclusion to be made here is concerned. Whichever choice is made results in the
*same* two numbers.

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