Page "Pascal's pyramid" Paragraph 30
from
Wikipedia
Writing the expansion in this non-linear way shows the expansion in a more understandable way.
It also makes the connection with the Tetrahedron obvious − the coefficients here match those of Layer 4.
All the implicit coefficients, variables, and exponents, which are normally not written, are also shown to illustrate another relationship with the Tetrahedron.
( Usually, " 1A " is " A "; " B < sup > 1 </ sup >" is " B "; and " C < sup > 0 </ sup >" is " 1 "; etc.
) The exponents of each term sum to the Layer number ( n ), or 4, in this case.
More significantly, the value of the coefficients of each term can be computed directly from the exponents.
The formula is: ( x + y + z )!
/ ( x!
× y!
× z!
), where x, y, z are the exponents of A, B, C, respectively, and "!
" means factorial ( e. g.: n!
=
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