230.00 Tetrahedral Number

230.01 Definition: The number of balls in the longest row of any triangular unit-radius ball cluster will always be the same as the number of rows of balls in the triangle, each row always having one more than the preceding row, and the number of balls in the complete triangular cluster will always be

\frac{(R + 1)^{2}- (R + 1)}{2}

Where:

R = the number of rows of balls, or the number of balls in the longest row

230.02 We can stack successively rowed triangular groups of balls on top of one another with one ball on the top, three below that, and six below that, as cannon balls or oranges are stacked. Such stacks are always inherently tetrahedral. We can say that the sum of all the interrelationships of all our successive experiences from birth to nowfor each individual, as well as forth e history of all humanityis always a tetrahedral number.