QUADRATICS ON THE PYTHAGOREAN ABACUS

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QUADRATICS ON THE PYTHAGOREAN ABACUS
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FINDING THE FORMULA FOR THE SQUARE OF A
BINOMIAL SUM
Since we know that X4 we can partition the root
factors of twenty-five into XY. So in this case
X4 and Y1. We can now see that the red
rectangle, equal X² is the product of the red
sections of base beads, equal X, and the single
blue bead rectangle, equal Y², is the product
of the blue sections of base beads, equal Y.  
The purple columns are each a product of one red
section, and one blue section of base beads so
equal 2(XxY). Therefore, (XY)x(XY)
X²2(YxX)Y². Thus we have the formula for the
square of a binomial sum.