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/sci/ - Science & Math

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2304563 No.2304563 [Reply] [Original]

just trying to figure out if this pattern of numbers has a name. it came to me years ago and i cant find anything on it. its just the multiplication table from 1x1 to 9x9. the sum of the 2 digits in the answer are added up. and it makes this pattern on to infinity. please let me know if anyone has heard of this. You can take any number, add the digits together of the number together. and keep adding those numbers up until you get a single digit, use this table, and the answer(once you have added the digits in the answer down till you get another one digit answer) will be the number in the corresponding column and row.

Examples:


7x3=21 (2+1=3) three is on the spot of 7 across and 3 down.

212x186=39432 (2+1+2=5 and 1+8+6=15, 1+5=6) go 5 across and six down you get 3. the answer 39432 is 3+9+4+3+2= 21 , 2+1= 3! See works every time for any number any size as long as you continually add the numbers in the problem and the answer down to a single digit. this could be used to check your work on any problem. As a side note, see the pattern all the different numbers make and how some are mirror images of other numbers

>> No.2304566

Yes, this is called multiplication modulo 9.

>> No.2304570
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2304570

>>2304566
\thread

>> No.2304581

thats awesome. thank you. ive had that in my head for YEARS and thought i was on to something big. figures math would have gotten to it first. what is the application of this? i mean what do you do with this?

>> No.2304588

>>2304570

Just to clarify, if you have *any* function that takes a number a to (a mod n), this multiplication table will hold. I didn't realize the process of going from multiple digits to single digits in this way was just finding the number mod 9, but now that you mention it it makes a lot of sense (inductive proofs are tedious but fairly easy)

>> No.2304596

>>2304581

Modular arithmetic is used in cryptography and in abstract algebra/topology/combinatorics. However, I notice that its main use (for myself) is in software and algorithms (i.e. computer science and engineering). Knowing how to encode the numerical equivalent of a circle with n states is surprisingly useful in a lot of ways.