Awatmath.1602
net.general
utcsrgv!utzoo!decvax!watmath!mabgarstin
Wed Jan 27 20:55:16 1982
more boring factorials, be forewarned
 This a simple relation to discovered in grade 10 and was published in a
nation-wide high school math rag to which I cannot remember the name.
 In my notation the > sign between lines means to take the difference
of the two numbers to which the arms of the > sign point back to. i.e.
      10
        >14         means 24-10=14
      24
 Sorry but this is the best way I pass this thing through the net.
 Lets start off with powers of 3.

0**3=  0
       > 1
1**3=  1   >6
       > 7  >6
2**3=  8   >12
       >19   >6
3**3= 27   >18
       >37   >6
4**3= 64   >24
       >61
5**3=125
 |
 |
etc.
 As you can that after THREE rounds of subtractions we got the number 6
or 3!.
 Lets try some others.

0**2= 0
      >1
1**2= 1  >2
      >3
2**2= 4  >2
      >5
3**2= 9  >2
      >7
4**2=16
 |
etc.
 With the power of 2 we 2 or 2! after only 2 rounds of subtraction.

0**1=0
     >1
1**1=1
     >1
2**1=2
     >1
3**1=3
etc.
  And with the power of 1 we get what we expect.
  Now lets try it for the power of 0.

0**0=????

 Welllll,...lets skip this particular value for now (Murphy's fudge factor
or Honsberger realignment procedure, something like that).

1**0=1
2**0=1
3**0=1

etc.

 Well now, with the power of 0 we 1 after 0 rounds of subtractions. Therefore
0! must equal 1 in order to satisfy this relation. (typo above, should be
'...of 0 we GET 1...').
 Try it out for powers of 4 and 5 if you have some time to waste like me.
You'll find things get strange when you hit powers of 7. For some reason
you have to take 8 rounds of subtraction to get 7! instead of 7. I haven't
figured that one out yet.
 Any memos, tips or other related ditties please mail to:

      watmath!mabgarstin   or   watarts!mab

    MAB Garstin at the Univ. of Waterloo


-----------------------------------------------------------------
gopher://quux.org/ conversion by John Goerzen <[email protected]>
of http://communication.ucsd.edu/A-News/


This Usenet Oldnews Archive
article may be copied and distributed freely, provided:

1. There is no money collected for the text(s) of the articles.

2. The following notice remains appended to each copy:

The Usenet Oldnews Archive: Compilation Copyright (C) 1981, 1996
Bruce Jones, Henry Spencer, David Wiseman.