¶ Number: Tetrahedral Number
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Index Entry
Number: Tetrahedral Number:
"N² - N is always a triangular number as, for instance, the
number of balls in the rack on a pool table. A telephone
connection is a circuit; a circuit is a circle; two people
need one circuit and three people need three circles, which
make a triangle. Four people need six circuits, and six
circuits cluster most economically and symmetrically in a
triangle. Five people need 10 private circuits, six people
need 15, and seven people need 21, and so on: all are
triangular numbers.
"Successive stackings of the number of relationships of our
experiences are a stacking of triangles. The number of balls
in the longest row of any triangular cluster will always be
the same number as the number of rows of balls in the
triangle, each row always having one more than the preceding
row. The number of balls in any triangle will always be
(R + 1)² - (R + 1) where R = the number of rows
2
(or the number of balls in the longest row)."
