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Topic: Names of polygons
Replies: 26   Last Post: Apr 29, 2008 12:08 PM

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Jeffrey C. Jacobs

Posts: 1
Registered: 12/10/04
More Knee Issues (was 11-gon)
Posted: Nov 29, 2000 8:17 PM
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Well, Prof. Conway, that was one of the more fascinating discussions
I've seen in Mathematics and Linguistics. One thing that's always
fascinated me about how the West and East developed is that at least
from Roman times, with I-V-X-L-C-D-M-Mbar and so on there was a clear
repetition every third digit (or 6 for the old British system). Thus
numbers start with their latin root and we have lovely things like
mi-llion, bi-llion, tri-llion and so on. Yet in the Far East, the
root has always been 4-digits. Thus you have a word for 1, 10, 100,
1000 and 10000. After 10000, you have 10 * 10000, 100 * 10000 and
then because no-one really needed numbers much greater than that until
recently they now conform to our 3-digit system of million, billion,
trillion. Now what you wrote of the Greek is interesting because you
imply that the Greeks followed a similar 4-digit system with
mono/hena, deca, hecta, chilia and myria, and what would come next?
Would we just say deca<times>myriagon or simply decamyriagon (10,0000
knees [note zero count intentional]) as opposed to myriadecagon /
myriakaidecagon for a 1010-gon? Did they have a word for 100,000 or
were they like the Far Easterners and had a 4-digit system in ancient
Greece, and if the later, did one influence the other or is it just
coincidence. I know the Mayans counted very large numbers based on 18
and 20 for their calendar but I'm not clear on any decimal pattern for
their larger numbers. Personally I've always found Base-210 very
interesting though as you could then determine divisibility of 2, 3, 5
and 7 by examining only the last digit and by 11 and 19 by summing the
digits and then finding if that number was divisible (the later rule
would work in the same way in Base-10 that we can add the digits of a
number to find divisibility by 3 or 9 since 10 - 1 = 9). Thanks again
for the fascinating discussion!

Be Seeing You,

Jeffrey.





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