The Number 6Date: 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! Please help me! 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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