This math scares me

[jurgen.defurne at philips.com]

It was the Babylonians who gave us the base-60 numbered
division of circular events.

Jurgen




grante at visi.com@SMTP at python.org on 15/03/2001 16:17:21
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Subject:	Re: This math scares me
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In article <mailman.984664520.26463.python-list at python.org>, Fabio Olive Leite wrote:
>Hi there,
>
>On Wed, Mar 14, 2001 at 09:31:54PM +0000, Grant Edwards wrote:
>) No.  The binary floating point representation of many decimal
>) fraction values is not exact.  That's what started this whole
>) thread.  You can't represent 0.1 exactly in binary FP.  You can
>) in BCD.
>
>Just to make matters worse in this discussion, let me add some more noise.
>
>Since base 10 contains base 2 and base 5 (`factor 10`), every
>number coming from any of those bases is exactly represented in
>base 10. Conversely, base 2 contains only itself, and thus it
>cannot represent correctly some numbers that are exactly
>representable in other bases, like 0.1 in base 10.
>
>The usual 1/3 example is a problem for base 10, but not so for
>base 12, for example, since 12 contains 3 2 2. Thus:
>
>1_{12} / 3_{12} == 0.4_{12}
>
>And then base 30 would let us count exactly fractions of base
>2, 3, 5, 6, 10, 12, 15, 16 and all the others you can think of
>that have only 2, 3 and 5 as factors of the base. But since no
>one (usualy) has 30 fingers, that base is not terribly popular.
>:)

One step further is base-60, which is still used for many
things.  Time and angular measurement for example is partially
a base-60 system.  I believe that one or more of the ancient
Aztecs/Incans/Mayans used a base-60 number system.

--
Grant Edwards                   grante             Yow!  It's hard being
                                  at               an ARTIST!!
                               visi.com
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