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### The Number 6

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Date: 07/24/97 at 05:57:14
From: kim
Subject: The number 6

I have been searching the net unsuccessfully for some information on
the number 6. Anything will do, but I can not find a thing!

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```
Date: 07/24/97 at 11:18:45
From: Doctor Rob
Subject: Re: The number 6

It is the first "perfect number":  it equals the sum of its divisors
less than itself:  6 = 1 + 2 + 3, and 1, 2, and 3 are all the divisors
of 6 less than 6.  The second one is 28 = 1 + 2 + 4 + 7 + 14.

It is a factorial:  6 = 1*2*3 = 3!

It is a triangular number:  6 = 3*(3+1)/2, which counts the number of
objects in a triangular arrangement of objects, 3 on a side:

O
O O
O O O

It is the number of subsets of size 2 which can be made from a set
of 4 different elements:  from {a, b, c, d} you can make {a, b},
{a, c}, {a, d}, {b, c}, {b, d}, and {c, d}.

It is the number of arrangements of three different objects in a row:
abc
acb
bac
bca
cab
cba

If you start with a number other than zero or one, and perform these
two operations repeatedly:

1) Subtract the current number from 1
2) Take the reciprocal of the current number

then six is the number of different numbers you can get (at most).
Example:  4 --> -3 --> -1/3 --> 4/3 --> 3/4 --> 1/4 --> 4

Enough?

-Doctor Rob,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
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