# The Number 5040

 Posts 181
Regular
jim
Regular
Joined: 8:19 PM - Apr 20, 2012
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

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


Obsessive poster
Obsessive poster
Joined: 11:27 PM - Sep 10, 2011
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
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Western encoding (not by choice)
Greasemonkey + Mathjax + PrimelDozenator
(Links to these and other useful topics are in my index post;
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 Posts 33
Casual Member
Einmaleins
Casual Member
Joined: 6:58 AM - Feb 12, 2018
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?

Obsessive poster
Obsessive poster
Joined: 11:27 PM - Sep 10, 2011
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)

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

 Posts 181
Regular
jim
Regular
Joined: 8:19 PM - Apr 20, 2012

Many people interested in the dimensions of the pyramids are aware that 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 = 36,280inches. 3,024 imperial feet the perimeter of the Great pyramid 756 x 4 = 3024 ft. They have flown past step 7 and 5040 and 2 stops later find themselves at the pyramid.

If anyone takes the time to read the short piece on doubling a cube into the shape of a pyramid they may realise I have used Indus Valley feet 13.2 inches in my example.

First of all it seems the ancients (because they did not possess electronic calculators preferred to arrive at even numbers and so used values for pi such as 22/7 and 3.14181818 to obtain them easily. For example 504 x 22/7 = 1584 792 x 2 = 1584. The question is could the imperial foot be an ancient measure? Here is one of many coincidences which I find interesting .

Imagine the third pyramid has a diagonal of 504 imperial feet and a circle is drawn around its base then the problem is to find the area of the circle in acres.

Diameter 504 imperial feet (458.181818 Indus feet 13.2ins)

504 / 2 = 252 squared = 63,504 square feet now to find the area of the circle multiply by 22/7 (remember the ancients did not have calculators so 22/7 widely used) = 199,584 square feet.

Now to find acres in imperial measure divide by 43560 = 4.58181818 acres. Same number as diagonal of pyramid in Indus feet 458.181818. Remarkable coincidence.

(Aside: 4.58181818 acres = 1.842 ha. In metric this has its origin in the base length of the pyramid 230.4 m Look 230.4 x 2 = 460.8 x 2 = 921.6 x 2 = 1843.2 or 1.8432 ha = 4.55459 acres = 198,397.94 square imperial feet / 22/7 = 63,126.61 square feet giving a side pyramid measure of 502.5 not exact but close to 504. Metric and imperial measure are in some way intertwined. I think.)

Same number as diagonal  504 imperial feet 458.181818 Indus Valley feet 13.2 inches. Readers have to decide for themselves if this is an accident or could the imperial foot be an ancient measures.???

Another interesthing question is the use of approximates in doulbling a cube as in my essay the base length of the third pyramid 324 and if a cube has a volume of 34,012,224 doubled = 68,024,448 cube root = 408.2144202.

Now for the ancients to do it approximately simple 324 x 1.26 = 408.24 for Great Pyramid .

We are able to arrive at 504 by 408.24 x 1.2345678999 = 504.

I don't understand that process however it works.

Jim