2. The pyramid
By turning the pyramid created (above) 90 degrees clockwise and slightly adjust it so that it
becomes vertically symmetric, the exponent-2 matrix will be like below, and maintain its
rules as built.
The aggregate exponent 2 pyramid (above) shows
The left pyramid is 3
, the right pyramid is 4
, and the whole pyramid is 5
. The overlap (intersect)
pyramid between 3
is also a square-number (2
) . As the pyramids are constructed, the
aggregate of the values in the rectangle at the bottom (2+2) has to be equal the overlap pyramid (2
which it is.
Let T be the aggregate value of all elements within the overlap/intersect pyramid.
Let R be the aggregate value of all elements within the “rectangle at the bottom”.
Because all elements in R are even (divisible by 2), R has to be an even square number (=T that is a
square number by definition/construction of the pyramid), all even square numbers from 4 an
upwards will generate Pythagorean Triples by use of the pyramid construction the following way:
Use an even square number as basis and divide it by 2 (common factor of all elements in R). From
this result create all rectangles with sizes that are factors of the result, including where one factor is
1. Let these factors be a and c. The Pythagorean triple (X, Y, Z) becomes :
(a + sqrt(R), c + sqrt(R), a + c + sqrt(R)).