Summial

 BBS: Inland Empire Archive
Date: 04-08-93 (18:11)             Number: 362
From: MICHEL BERTLER               Refer#: NONE
  To: EARL MONTGOMERY               Recvd: NO  
Subj: Summial                        Conf: (2) Quik_Bas
 EM> I was fooling around with writing a formula to figure the total
 EM> # of blocks required to build a pyramid as described below.
 EM> Notice each descending row has 1 more block than the level
 EM> above. I do NOT have a background in math! But I saw a
 EM> relationship and came up with this formula:

 EM>                                        .
 EM>                                       . .
 EM>                                      . . .
 EM>                                     . . . .
 EM>                                    . . . . .
 EM>                                   . . . . . .
 EM>                                  . . . . . . .
 EM>                                 . . . . . . . .
 EM>                                . . . . . . . . .
 EM>                               . . . . . . . . . .


It's the `summial' where:  = n(n+1)/2

In the above formula, `n' is the number of rows of dots
from any summit of the triangle to its opposed side and `'
(sigma) is the total number of dots.

10(10+1)/2 = 55

This could also be easily verified by long addition:

1+2+3+4+5+6+7+8+9+10 = 55

The same formula could also be written as:  = (n+n)/2

 EM> Earl's Law <smile>
 EM> Total Blocks=Level * Level value
 EM> Level         Level value
 EM> 1             1
 EM> 2             1.5
 EM> 3             2
 EM> 4             2.5
 EM> 5             3
 EM> 6             3.5
 EM> 7             4
 EM> 8             4.5
 EM> 9             5
 EM> 10            5.5

 EM> My question is: Is there a math rule similar to this? And if so
 EM> what is it called?

By recurrent definition I would say: (L+1)/2 = Lv, where L
stands for `Level' and Lv for `Level value' from `Earl's
arithmetical suite'!

Keep in mind that sommial & factorial are both arithmetical
suites only dealing with integers!

Michel

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