[2017-04-20] Satan fingers

Blame Quintushalls for this.

Moderator: Kimra

[2017-04-20] Satan fingers

Postby Schaaschaa » Tue Apr 25, 2017 8:23 pm

Sorry for being overly pedantic, but I don't agree.

It's not so much a property of nines as a reflection of the fact that we happen to use a number system that's based on the same number as the number of fingers most of us have. If we had 12 Fingers, the magical number would be 11.

In fact, if you're prepared to describe the rules a little more precisely, it actually works for a lot more numbers.

Say n is the base of your number system and also the number of fingers you have. You can now accomplish this feat with any number a < n. You can figure out the product of a*x for any x element of N, for which x*(n-(a+1))+x <= n is true by holding up finger number x and after that one x*(n-(a+1)) more fingers.

In our world, n = 10. In the comic, a = 9. In the first example, x = 5, so you have to hold out finger number 5 and after that one 5*(10-(9+1)) = 5*(10-10) = 5*0 = 0 more fingers. In the second example, x = 9, so you hold out finger number 9 and 9*(10-(9+1)) = 0 more fingers. For a = 9, it breaks down after x = 10, because 11*(10-(9+1))+11 <= 10 is no longer true. Basically, you run out of fingers. The built in zero is what makes the number 9 so special.

If you want to figure out 3*8, you hold out your 3rd finger and 3*(10-(8+1)) = 3*(10-9) = 3*1 = 3 more. VoilĂ , you get 24. It works for a = 8 until x = 5, for a = 7 until x = 3, for a = 6 or 5 until x = 2, for any smaller a only for x = 1. It even works for a = 0.

Now say we only had 8 fingers and our number system would be based on the number 8. If you now want to figure out 2*5, you hold out your 2nd finger and 2*(8-(5+1)) = 2*(8-6) = 2*2 = 4 more. Now you have one finger on one side and two on the other. Since our number system is now based on 8, this works out to be 8 * 1 + 2 = 8 + 2 = 10, which really is 2*5.


I'm kinda fascinated :lol: And yes, I did create this account specifically for making this post.

Sorry. I hope I didn't accidentally break any rules doing this ^^
Schaaschaa
 
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