In case you decide to have different peoples use different bases for their numeric systems in your world, as I did, I thought it might be helpful to tell you how I switch numbers between bases. * smiles * It took me awhile to work out the best way of doing it.

There are basically two systems I use. The reason I don't only use one is because different ones work better for different things. One of them makes it easy to switch from the new number base (hereafter referred to by the variable N) to base 10, the other works best vice-versa. If you use both it makes it so you don't have to do any math operations in N, which are difficult to do, if you are not used to it. Especially long-division....

So, the first one, for switching from base 10 to N (Both methods work whether N is larger than base 10 or smaller):

1) You divide, in base 10, the number you wish to translate (hereafter referred to as x) by N.

2) Take the remainder, and write it down as the smallest digit of the translated number (even if it is 0, as you might guess).

3) Divide the answer to your last problem by N.

4) Repeat step 2.

5) Repeat step 3.

6) Continue repeating until the answer is too small to divide by N, then place it as the largest digit of the translated number.

And...that's it.

Note, though, that if N is greater than base 10, you must use letters or something else to stand for the numbers between. 10, 11, and so forth.


The next system, for translating a number in N to base 10:

1) Make a table of the base 10 equivalents of 10, 100, 1000, and so on as far as you need, in N. (This is easy, it only involves multiplication, you know.)

2) Divide x into its addends, by places. For example, 1275 equals 1000+200+70+5.

3) Multiply the equivalent of each place by the number of them that there is in each addend of x. Does...that make sense? Basically if you take the thousands addend, you look at how many thousands are in it (three thousands in 3000, you know), and multiply that by the equivalent of a thousand on the table you made.

4) Add all the converted addends.

And there's your number.


I will try to give more explanation if someone wants it.* smiles * I love math.

*scrambles around, scouring the HW rules, along with old policy threads* I could've sworn it was against some natural law to bring math into HW!

* glares * If there is, then – then – * splutters * I can't live without math! It's one of the funnest things I do! The only thing I have ever had to complain about math is that we don't have the money right now to buy a text on advanced calculus! I write poetry about math! I dream about math! Zero is one of my best friends!

Oh my...

I had never even considered having a different numerical system.

*will have to examine this in detail sometime soon* I love doing stuff with math.

My one half-project has been to figure out the Earth math for a system based on pi.

It's an interesting detail to consider.



A...system of what? * slightly bewildered * A numeric system? 0.0

No... just thinking math through as if pi had the value of 1. And then thinking of the cultures that would use math like that.

One language I worked on in middle and high school counted in base 7.


I can't imagine any way that could work; irrational numbers are useful in many contexts for describing phenomena that the rational numbes alone cannot, but the only useful expression I know of that doesn't use rational numbers is Euler's identity (e-to-the-quantity-pi-times-i-equals-negative-one). But if you can imagine how it might work, more power to you!

It's possible that I'm completing messing up the math.

Pi...can't have the value of one. because it isn't one. * lop-sided grin * So – are you meaning that this culture divides their number-line into periods of the length of the value of pi? * interested *

Maybe this conversation should continue elsewhere, somewhere or other...I think it's de-railing the thread. It's too interesting!

Sorry about that.

Sooo... are you going to talk to me about it somewhere else? * hopeful look * You can't just intrigue me like this and then leave me hanging!