Mathematics: Mod...

It's the remainder of 334/11.

334/11 = 30 with a remainder of 4.

 

Keep it on Scientific Calculator setting... XDecimal, XDegrees

Watch your calculator while you do this:

(press) 334
(Hold shift key, press) %
(press) 11
(press) =
4

 

Mod is a function used when a problem uses numbers which "cycle back around". BTW - you already know how to do this! You just didn't know what it was called. An example is the dial face of a 12-hour clock. If it's 9 o'clock, and someone says, let's meet in 4 hours, you know they mean 1 o'clock.

(9+4) mod 12 = 1.

 

Probably somebody who got pissed off solving for remainders in grade 5 math class.

 

If you want to slow somebody's computer down, punch up

numbers
Mod
numbers
n! button
n! button
=
n! button

hehehehheeeeeeehehehe

 

Cool!

 

My example was that 9 o'clock plus 4 hours is "13 o'clock", but that's the same as 1 o'clock. Hence 9+4 mod 12 = 1.

Our 12 hour system works on arithmetic mod 12. The military 24 hour system works on arithmetic mod 24.

Same with a crankshaft and 720 degrees (2 full rotations for a complete 4 cycle). That's a system using mod 720 arithmetic. When a crankshaft is at TDC and the crank is rotated 725 degrees, this is the same as TDC + 5 degrees (rotating 720 degrees takes you back to the same crank and camshaft positions, then you went 5 degrees further).

 

I just realized why you're asking about mod 11...

You need it to calculate the check digit in a VIN!!!

That's yet another use. See modulus arithmetic is all over the place

 

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Darth, LoL!

 

Just did some new math: (2+2) mod "NNO" = "VIN" !

There aren't too many things that require mod 11 arithmetic, VIN's is one that I knew. It's you asking, so VIN makes perfect sense for that reason. Why I know that VIN's use mod 11 for the check digit goes back to that e-mail I sent you several months back.

 

Hi Carbon,

To answer your question about who came up with this kind of thinking and what does it serve, well, I don't know who came up with it but its used for calculating a check digit (someone mentioned that but didn't go into details) and the most common use of this is in vehicle VIN numbers and also credit card numbers.

The idea is to churn a serial number through a process that slightly modifies the number, and add that modification onto the end (normally). Then, because you can re-create the last digit from the rest of the number, this gives you a chance to 'check' the number hasn't been tampered with or just plain made-up.

A good example is in credit card systems where you phone up the CC company and get the interactive voice response (IVR) prompt you for your card number. It does the math on the number you gave it and if you've mis-typed or are some kind of fraudster using a made-up number, the IVR itself knows straight away that there is no point even trying to look up your balance & account details etc because the number is duff.

There is a complemetary function to mod, called div, which is just how many times the number you give it fully divides into the first number, rather than giving the remainder, like mod does.

334 mod 11 = 4 (as stated previously)
334 div 11 = 30

That should help!

Regards,

Rich.

 

BTW - Modular arithmetic was introduced by Carl Friedrich Gauss in his book Disquisitiones Arithmeticae published in 1801. However, people were using it before then (e.g. clock arithmetic as discussed), just not formally.

 

As an aside, I'm pretty sure credit cards use this function as well..to arrive at the 14,15, or 16 digit number.

 

Us computer programmers use it quite a bit. I forget why but I know we do.

 

Encryption - http://www.krellinst.org/UCES/archive/modules/charlie/pke/node2.html

Music
The scale is mod 8.

and if you REALLY want to get into it
http://www.cse.nd.edu/courses/cse20211/www/Ex2-ReviewProb.html

 

For starters, it is used a lot in cryptography. For example, the SSL connection that your web browser makes for that online purchase also uses the same modular mathematics.