🛠 Interactive Tools
These tools illustrate key ideas in sacred arithmetic: power cycles modulo 9, number vortexes, theosophical reduction, and number sequences. Each tool includes a short explanation of what it demonstrates.
🔢 Power cycle (mod 9)
Choose a multiplier from 1 to 9. The tool shows the sequence of powers (n, n², n³, …) reduced modulo 9: at each step you multiply by the same number and keep only the single-digit root (1–9). You see how a number eventually returns to itself in single-digit arithmetic — the cycle length depends on the multiplier.
🌌 Sacred number vortex
A spiral visualization of famous sequences: 3-6-9 (Tesla reference), the repeating cycle of 1/7 (142857), and the ×2 duplication cycle in mod 9 (1, 2, 4, 8, 7, 5). Each sequence forms a closed loop when reduced to single digits.
📐 Digital root (practice)
Theosophical reduction means adding the digits of a number, then repeating until you get a single digit (1–9). Example: 284 → 2+8+4 = 14 → 1+4 = 5. A random number is given; find its digital root.
Digital root of: —
🎼 Number sequence
Enter a list of digits separated by commas (e.g. 1,2,4,8,7,5). This tool is intended to link a sequence to a sound or visual pattern — mod 9 cycles can be explored as numerical melodies.