ARRANGEMENTS OF TRIANGULAR NUMBERS
Triangular, pronic, and square numbers all result from adding successive sets of counting, even or odd numbers. Pronic numbers are double the value of triangular numbers whereas square numbers result of adding two successive triangular numbers together.
TRIANGULAR ARRAYS
The arrangements of blocks in the table above highlight the progression of triangular numbers and its multiples. Each column doubles the amount of blocks from the previous column. Note how x8 triangular numbers forms an odd square number -1.
SQUARE ARRAYS
The arrangements of blocks in the table above highlight the progression of square numbers and its multiples. Each column doubles the amount of blocks from the previous column.
LINEAR SCALE
The square spiral scales to any unit length. The top most spiral counts one unit of length for every grid cell, the next counts one unit of length for every two grid cells, and the last counts one unit of length for every four grid cells. The sequences of numbers generated diagonally across the spiral array scale down proportionally as well.