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CONLANG  June 1999, Week 2

CONLANG June 1999, Week 2

Subject:

Conmath (Re: ConNumbers)

From:

David Crowell <[log in to unmask]>

Reply-To:

[log in to unmask]

Date:

Fri, 11 Jun 1999 02:06:54 +0000

Content-Type:

text/plain

Parts/Attachments:

Parts/Attachments

text/plain (73 lines)

A system based on pi or e might be impractical but here are a few
ways to represent fractions.

I have created a conmath with a complete binary arithmetic
and representation of numbers, but it is easier to work with
than with all 1's and 0's.,


Definitions of mathematical terms with # appear before the quoted text
which happens to be at the end of the message.

The way the Egyptians indicated fractions is by adding reciprocals#
of whole numbers  and or 2/3.
2/5=1/3 + 1/15

In a computer programming magazine (long time ago, way before
Windows), I saw a program of a neat way to represent numbers.
The digits left of the whole/fraction point are multiplied/divided by the
factorial# of the number of the digits from the w/f point.
4321.1234
4*4!+3*3!+2*2!+1*1! + 1/2! + 2/3! + 3/4!
96+18+4+1 + 1/2 + 1/3 + 1/8=119+23/24
Adding and subtracting can be done in this method,
but not multidigit multiplying/dividing.
However, all {rational numbers} can be (in theory, if not
practically) represented by a finite number of digits.
   Note:  .x(y)+ means that the digits in (y) repeast without end.
1/7 (decimal) = 0.142857(142857)+ (decimal) = 0.003206 (factorial-math)

There is also a neat way to represent fractions.
The fractions are called continued fractions.
To get a continued fraction:
1 Seperate the whole part from the fractional part. e.g 67/29=2  +9/29
2 Take the reciprocal of the fractional part. eg. 1 divided by 9/29=29/9
3 Repeat steps 1 and 2 to the reciprocal of the fractional part until there
is no fractional part left. eg. 29/9=3  +2/9
    9/2=4  +1/2
    2/1=2  + 0 (done)
4 Put each whole part of the numbers in an ordered list. 67/29=[2, 3, 4, 2]
All rational numbers can (practically) be presented by a finite list.
But, unfortunately,  calculations with the continued-fraction lists are not
practical.


reciprocal - The quotient of a specific number when one is divided by it.
 The reciprocal of x is 1/x

rational number - any number that can be represented by an integer# or quotient of

an integer divided by a {whole number}#(see integer below)
5, 2/5 and 1/10 are all integers.

integer - Any number in the set of positive who numbers (1, 2, 3, ...) or negative

whole numbers (...-3, -2, -1) and zero (0)

Tom Wier wrote:

>
> Here's a system I've never seen worked out, or even heard of:
> a system based on pi, or e, or other irrational numbers like that.
> Anyone want to take a crack at that?
>
> ===========================================
> Tom Wier <[log in to unmask]>
> AIM: Deuterotom ICQ: 4315704
> <http://www.angelfire.com/tx/eclectorium/>
> "Cogito ergo sum, sed credo ergo ero."
>
> "Things just ain't the way they used to was."
>      - a man on the subway
> ===========================================

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