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: ä = 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 `ä'
(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: ä = (ný+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
--- GoldED
* Origin: Blainville, Quebec (1:242/130)
