Using Base 10 to Calculate Vortex Sum of Different Number Systems

In this video I show that the vortex digit sum (summing the digits until we obtain 1 digit) for any base number system can be obtained quickly by using the default Base 10 Modulo function available in most calculators. For most number systems we need to first convert to the number to its base 10 equivalent before inputting into the calculator, which we can convert via writing as its powers of 10 addition form. However, for the base 4 number system, since the largest single digit 3 is a factor of 9 (largest single digit in base 10), the base 10 mod function gives the same result without conversion! Pretty amazing stuff!

#math #vortexmath #modulararithmetic #numbertheory #education

8 Base 10 Conversion.png

Timestamps

Base 10 is most widely used base number system – 0:00
Modulo function in Microsoft Excel and OneNote are in Base 10, so need to convert bases – 0:23
123456 (base 7) v= 3 – 2:08
Base 7 is smaller than Base 10, so modulo function gives identical results in base 10 – 5:01
For Base numbers larger than 10, the remainder can be in double digits – 6:12
For convenience, I will write all base number systems as their base 10 equivalent – 8:23
Can calculate Base 4 vortex sum using Base 10 mod function without conversion – 11:16
Base 8 requires conversion because 7 is not a factor of 9 – 12:06
Base 4 doesn't require conversion because 3 is a factor of 9 – 13:19
Modulus 3 (base 4) is factor of modulus 9 (base 10) – 14:48
Comparing with and without conversion of base 4 using base 10 mod function – 16:17
All numbers used are by default in Base 10 unless stated otherwise – 19:39