Multiplying a Number and Its Vortex Sum Results in the Same Vortex Sum

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In this video I show that multiplying a number or its vortex sum (summing digits until a single digit is obtained) yields the exact same vortex sum. This is the cause of nearly all of the amazing vortex math patterns! I derive why this is the case, which works for any integer multiple and any general base number system, by showing that the multiples always yields a factor of 9 (or base - 1) plus the remainder multiple. Thus the remainder governs the vortex pattern. And since final remainder is a single digit, which is limited to the base number system, then it means we will ALWAYS have a repeating pattern regardless if the multiplying numbers grow very large. Quite fascinating!

#math #vortexmath #modulararithmetic #numbertheory #education

9 Vortex Sum Multiplication.png

Timestamps

Factor of 9 means whole number can be divided cleanly by 9 – 0:00
Writing numbers as factors of 9 results in the remainder being the vortex sum – 0:57
11 and 11 * 6 are both written as factors of 9, and remainder governs vortex sum – 2:54
Multiplying 11 or its vortex sum 2 by 6 results in the same vortex sum! – 3:58
Proof for any integer and base number system – 4:52
Multiplying an integer by another integer still yields a factor of (base - 1) – 7:20
Vortex sum is same as vortex sum of the multiple – 11:29
Example: (base 10) 17 * 4 v= 8 – 12:30
Example: (base 8) 15 * 4 v= 3 – 15:00
Easier to just determine the vortex sum of the remainder as numbers get large – 21:24
This is the causation of most vortex math patterns! – 23:39
Infinite numbers but only a finite number of single digit base numbers – 26:16