Monday, August 23, 2004

7 Mathematical Sins

For those of you not attuned to the world of numbers, bear with me hear.

I have often been heard to state (usually when drunk) that maths is the universal language that would be used for communication with aliens, if such things existed. (I also siad that linguistics is what would poison the process, but I know I was being a divot). This can in part explain why I wanted the domain etotheipi.com originally, but someone beat me to it (for those that don't know, check the site for why this name is nice).

Anyway, back in my primary school days, being taught times tables, my teacher at the time told the class that the 9 times table is easy to remember, because if you take the digits of any answer between 1 and 10, they add to give 9.

If you've never noticed this before, check: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90. It works.

A slight extension to this idea will give the same result for every poistive multiple of 9. Example: 9*11 = 99. Add the digits to get 18. Add those digits together to get 9.

I always thought this was a nice little twist to the world of numbers. Then sometime in secondary school I noticed a little trick with the 7 times table. Adding the digits together for these values gives an odd-even countdown kind of thing. Observe:


07, 14, 21, 28, 35, 42, 49, 56, 63, 70 GIVES:
7,, 5,, 3,, 1,, 8,, 6,, 4,, 2,, 9,, 7


Again, this sequence repeats for quite a while. Cut to yesterday, when this quirk pops into my head again. I wondered if this would extend to other number bases. If you use hex encoding, you get:


Decimal: 07, 14, 21, 28, 35, 42, 49, 56, 63, 70
Hex:.... 07, 0E, 15, 1C, 23, 2A, 31, 38, 3F, 46
Added:.. 7,, E,, 6,, D,, 5,, C,, 4,, B,, 3,, A


A swapping countdown. I haven't tested this further than 10, because Excel on this machine is severely lacking in hex tools.

The 9 rule is also adaptable. Using hex again, and F instead of 9, all positive multiples of F give answers whose digits add to give F.

Right, I'm sure that bored the hell out you, but you've read it, and you can't unread it!

2 Comments:

Anonymous Anonymous said...

... Only 20% in that geek test then Stevo?

But as a computing scientist surely you should see at as all things being able to be represented in binary code? Of course, making that an extension to mathematics...

Maybe not.

KG

12:13 am  
Blogger Chris said...

"Right, I'm sure that bored the hell out you, but you've read it, and you can't unread it!"

Very very true! As in it did bore the hell out of me and I am having a hard time trying to unread it.

8:14 pm  

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