The Number 5040

The Number 5040

jim
Regular
jim
Regular
Joined: Apr 20 2012, 08:19 PM

Apr 2 2018, 10:46 AM #1

Years ago when I became interested in ancient measures the first to mark my paper was a gentleman named Garnett Greenbury. He knew I was not a math person but still he was a very unusual gentleman and he said to me if you ever come across this number 5040 please let me know.

It has been staring me in the face for years.

Many people accept 756 imperial feet as a measure for the length of the Great Pyramid and believe it equates to 440 Royal cubits. I don't believe that is correct but in any case I had realised that the diagonal of the Great Pyramid was 3 times that of the base length of the 3rd Pyramid. I. E. S . Edwards the 'Keeper of Egyptian antiquity' at the British museum had written that the base length of the 3rd pyramid = 356.5 feet and this I realised was 1/3rd of the diagonal of the Great Pyramid.


To cut this short and for interest 756 feet produces a diagonal for the Great Pyramid is 1069.145453 imperial feet and 1/3rd of that figure = 356.3818177 Imperial feet.

The diagonal then of the 3rd pyramid = 504 imperial feet and I hope those of you who are interested will enjoy the number. The birth of some remarkable numbers. How did the ancients know this???

https://joedubs.com/5040-the-perfect-number/

Jim

 
Reply
Like
Share

icarus
Dozens Demigod
icarus
Dozens Demigod
Joined: Apr 11 2006, 12:29 PM

Apr 3 2018, 04:57 PM #2

5040 is the 19th highly composite number and the 8th superior highly composite number; it is the factorial of 7 and Plato was pretty fond of it. The ancients might not have had Twitter and Netflix but they did have a brain every bit as quick as our own, and their memories were superior to our own. Dozenally, the five dozen factors of 2b00 (z) = {1, 2, 3, 4, 5, 6, 7, 8, 9, a, 10, 12, 13, 14, 16, 18, 19, 20, 24, 26, 2b, 30, 34, 36, 39, 40, 48, 50, 53, 5a, 60, 68, 70, 76, 89, 94, a0, a6, b8, 100, 120, 130, 156, 180, 190, 1b4, 223, 240, 260, 2b0, 360, 3a8, 446, 500, 5a0, 700, 890, b80, 1560, 2b00}.

Below: columns are the index n, highly composite numbers, if the number HCN(n) is a superior highly composite number, the index of that number appears in the 3rd column. In the fourth column we have the number j of which HCN(n) is a factorial (j!). In the last column we have the exponents of the prime factors of HCN(n). 5040 = 2^4 × 3² × 5 × 7 = 4.2.1.1. All the preceding HCNs in the list divide 5040 evenly, i.e., they are divisors of 5040. It is a keen number.

Code: Select all

 n     HCN(n)   i    j    MN(HCN(n))
 1         1         1    0    
 2         2    1    2    1    
 3         4              2    
 4         6    2    3    11   
 5        12    3         21   
 6        24         4    31   
 7        36              22   
 8        48              41   
 9        60    4         211  
10       120    5    5    311  
11       180              221  
12       240              411  
13       360    6         321  
14       720         6    421  
15       840              3111 
16      1260              2211 
17      1680              4111 
18      2520    7         3211 
19      5040    8    7    4211 
20      7560              3311 
21     10080              5211 
22     15120              4311 
23     20160              6211 
24     25200              4221 
25     27720              32111
26     45360              4411 
27     50400              5221 
28     55440    9         42111
29     83160              33111
30    110880              52111
31    166320              43111
32    221760              62111
33    277200              42211
34    332640              53111
35    498960              44111
36    554400              52211
Reply
Like
Share

Kodegadulo
Obsessive poster
Kodegadulo
Obsessive poster
Joined: Sep 10 2011, 11:27 PM

Apr 3 2018, 11:17 PM #3

Note that all the properties of this number, and its relatives, which icarus has cited here, are purely mathematical in nature, and hence universal. That means that any civilized species of intelligent life, on any planet in the galaxy, regardless of biology or technological achievement, can readily discern and appreciate those properties, in complete disregard of any of the more trivially obscure associations we petty humanoids might endow them with, infatuated as we are with the "cleverness" of the various unremarkable piles of rocks our several primitive tribes have strewn about this mediocre planet, over our geologically fleeting existence.
As of 1202/03/01[z]=2018/03/01[d] I use:
ten,eleven = ↊↋, ᘔƐ, ӾƐ, XE or AB.
Base-neutral base annotations
Systematic Dozenal Nomenclature
Primel Metrology
Western encoding (not by choice)
Greasemonkey + Mathjax + PrimelDozenator
(Links to these and other useful topics are in my index post;
click on my user name and go to my "Website" link)
Reply
Like
Share

Einmaleins
Casual Member
Einmaleins
Casual Member
Joined: Feb 12 2018, 06:58 AM

Apr 4 2018, 07:56 AM #4

Kodegadulo wrote:  this mediocre planet, over our geologically fleeting existence.
I would not call this planet mediocre! But perhaps you are more of a pessimist?

It matters so much what funny ideas people hav about numbers (and pyramids)? if it amuses them, who are we to criticize and spit on them?
Reply
Like
Share

Kodegadulo
Obsessive poster
Kodegadulo
Obsessive poster
Joined: Sep 10 2011, 11:27 PM

Apr 4 2018, 03:13 PM #5

Einmaleins wrote: I would not call this planet mediocre! But perhaps you are more of a pessimist?
Well it might not be mediocre to us, since we live here, but we ought to guard against delusions of grandeur about the cosmic significance of purely parochial matters, and instead look for what is
actually of cosmic significance. One might fancy one's world as Brobdingnag, but from a broader perspective it might merely be Lilliput.
It matters so much what funny ideas people hav about numbers (and pyramids)? if it amuses them, who are we to criticize and spit on them?
Just trying to highlight the contrast between two completely different approaches to discovering the significance of numbers...
As of 1202/03/01[z]=2018/03/01[d] I use:
ten,eleven = ↊↋, ᘔƐ, ӾƐ, XE or AB.
Base-neutral base annotations
Systematic Dozenal Nomenclature
Primel Metrology
Western encoding (not by choice)
Greasemonkey + Mathjax + PrimelDozenator
(Links to these and other useful topics are in my index post;
click on my user name and go to my "Website" link)
Reply
Like
Share

icarus
Dozens Demigod
icarus
Dozens Demigod
Joined: Apr 11 2006, 12:29 PM

Apr 5 2018, 01:33 PM #6

While I might not ascribe overmuch significance to ancient pyramids, still fascinated as anyone ought to be by the organization and the construction technique, the sacrifice to the sacred of their time, I think it's fair to think of what-ifs regarding how the ancients might have rationalized number. They weren't as bound to a strict tradition that maths or science is today. Astrology and astronomy were intertwined and the Greek techne, craft, was art and technology all at once. I am not saying it is a good thing to continue with the fusion of the metaphysical and physical, but that it releases the mind to consider how something might be put together in order to consider further possibilities.

I don't think humanity is random or our existence casually puny. You don't react that way caught in traffic. You have a purpose. You also take care not to get in an accident, for it might cost life. So it must be worth something. We are formidable and brilliant creatures. I think that people are the very most fascinating thing in the universe, and that the earth, though there may be similar "habitable" worlds around similar stars, we know of only one with sentient intelligent life, possibly more than one variety, and that is sheerly amazing. More amazing than degenerate matter in neutron stars or charmonium. And I wouldn't look down upon what our forefathers wrought. How old is the Sphinx? That is a good question. Did it predate the Younger Dryas? What does it mean? People don't build things for no reason at all, to honor randomness, but for a purpose. This includes dimensions and systems. These bases may not be the ones we might use; we might base our systems on scientific or traditional measures; the ancients had other reasons. Not sure they were number-theoretical, but I think deep thinkers might have just been plain fascinated with a highly divisible number. Child's questions, because children are not bound to convention. No I do not like cranks, but I don't mind exploring something. All we are doing here is exploring tantalizing what-ifs and maybes.
Reply
Like
Share