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Is there a mathematical theory for this phenomenon?
#1

Is there a mathematical theory for this phenomenon?
Surely I cannot be the only one who has ever recognized it.

Let's just start with a high number to follow the pattern. What we're doing is adding up the digits.

210 = 3
211 = 4
212 = 5
213 = 6
214 = 7
215 = 8
216 = 9
217 = 10 = 1
218 = 11 = 2
219 = 12 = 3
220 = 4
221 = 5
222 = 6
223 = 7
224 = 8
225 = 9
226 = 10 = 1
227 = 11 = 2
228 = 12 = 3
229 = 13 = 4
230 = 5
231 = 6

Etc and so on.

Interesting, right?
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#2

Is there a mathematical theory for this phenomenon?
[Image: 96ed57d114ff36d49c82f42f8287791c.png]
Contact this guy (555)123-4567
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#3

Is there a mathematical theory for this phenomenon?
Wait 'til you discover the multiples of nine.
Freedom isn't free.
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#4

Is there a mathematical theory for this phenomenon?
Modular Arithmetic. It works in other bases as well, if one uses different symbols for the digits, like hexadecimal (or base 12 like the clock example at this wikipedia entry).

https://en.wikipedia.org/wiki/Modular_arithmetic
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#5

Is there a mathematical theory for this phenomenon?
It's called the digital root and is found by adding all the digits of a number together until you are left with a single digit number.

As Thump alludes to, it can be handy for finding multiples of 3 and 9 in base 10. If the digital root is divisible by 3 then the original number is divisible by 3. If the digital root is 9 then the original number is divisible by 9.

e.g.: Is 123,456,789 divisible by 9?
1+2+3+4+5+6+7+8+9 = 45, 4+5 = 9, so yes 123,456,789 is divisible by 9.
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#6

Is there a mathematical theory for this phenomenon?
(04-26-2020, 07:01 PM)Paleophyte Wrote: It's called the digital root and is found by adding all the digits of a number together until you are left with a single digit number.

As Thump alludes to, it can be handy for finding multiples of 3 and 9 in base 10. If the digital root is divisible by 3 then the original number is divisible by 3. If the digital root is 9 then the original number is divisible by 9.

e.g.: Is 123,456,789 divisible by 9?
1+2+3+4+5+6+7+8+9 = 45, 4+5 = 9, so yes 123,456,789 is divisible by 9.

Set your alarm clock for 7 am. Set the snooze for 9 minutes. Alarm goes off at 7, hit snooze. It'll go off at 7:09. Hit snooze again and it'll go off at 7:18 (1+8=9). Hit snooze again, it goes off a 7:27 (2+7=9). follow the series, it will always add up to 9 through the hour. It's that one-off thing.
Freedom isn't free.
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#7

Is there a mathematical theory for this phenomenon?
(04-26-2020, 11:31 AM)Phaedrus Wrote: Interesting, right?

Thanks for that.  Interesting, yes, but not really surprising.
If you add up all the digits of any number until you end up with a single digit, the only single digit you can end up with is between 1 and 9.  Adding 1 to the original number will add 1 to the sum.  So, you will automatically cycle through those nine digits from any starting number you choose and going up by 1 at a time.   Smile
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#8

Is there a mathematical theory for this phenomenon?
(04-26-2020, 11:31 AM)Phaedrus Wrote: Surely I cannot be the only one who has ever recognized it.

Let's just start with a high number to follow the pattern. What we're doing is adding up the digits.

210 = 3
211 = 4
212 = 5
213 = 6
214 = 7
215 = 8
216 = 9
217 = 10 = 1
218 = 11 = 2
219 = 12 = 3
220 = 4
221 = 5
222 = 6
223 = 7
224 = 8
225 = 9
226 = 10 = 1
227 = 11 = 2
228 = 12 = 3
229 = 13 = 4
230 = 5
231 = 6

Etc and so on.

Interesting, right?

Each number is the previous plus one.  All else follows.
Philosophy is about asking questions.
Science is about answering questions.
Theology is about avoiding questions.
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