The tetractys is the earliest famous example of a figurate number, a number shown as a shape. Set out one point, then a row of two, then three, then four, and the total, ten, appears as an equilateral triangle; the Greeks called such totals triangular numbers, and the tetractys is the fourth of them. The figure rewards contemplation in more directions than one. Read downward it was taken as a generative sequence: the single point stands for the monad, the pure unit; two points determine a line; three, the first surface; four, the first solid, since four points not in one plane define a tetrahedron. In four steps the figure walks from unity to body, from the One to the world of extended things, which made it a diagram of emanation as much as of arithmetic. Read as ratios between its rows it holds the musical concords, and read as a sum it delivers the decad, the number the school held perfect and complete.
Burkert's reconstruction of early Pythagoreanism shows this arithmology already interwoven with the school's religious life, transmitted in the acusmata alongside rules of diet and burial, which is to say that for the Pythagoreans it was never mathematics on one side and piety on the other. The tetractys stands at the head of a long tradition, running through Neopythagorean and Platonist number lore into the number mysticism of the West, in which the first ten numbers are not quantities but powers, and this atlas's entries on those numbers walk in its shadow.