Second Communication

B) SECRETS OF PI 

(Continuation)


1) In the previous communication I`ve said that the first 100 decimals of Pi did sum 477. And that this number was in relation with the Great Pyramid. In fact, in an occult manner.
I explain:

2) The vertical section by the median of the base of that pyramid is an isosceles triangle with the proportions of 14:22 (fig 1).

Figure 1

Or there exists a second isosceles triangle and only one with height and base in whole numbers (21:12) that, superposed to the first, gives at the intersection points with it values of 22/7. The oblique side of this second triangle takes the value of square root of 477 (fig. 2).

Figures 2 and 3


3) Otherwise, we have a third isosceles triangle and only one with height and base in whole numbers (22:14) that share with the first the same inscribed square (fig.3).

4) These three triangles, with such an exclusive geometric relationship, have respectively, areas of 154, 126, and 154.
The sum of these areas is 434.

5) We`ll see now an unexpected coincidence with the 3 numbers that compose the "Singularity of Pi": 5, 761, and 239 (V/ "First communication").
So:

1st Formula

This equation, strangely, has a relation with the expression showed in paragraph 2 of the "First communication", that points out another particularity of pair 761 - 239.

6) Note that, in fig.3, the circle with radius AS and the square NPQR they have same perimeter (in similarity with the Great Pyramid, where the circle with radius equal to the height has the same perimeter of the base):

2nd Formula


7) It`s, perhaps, interesting to remind the formula used by John Machin (1706) for the calculation of Pi:

Pi = 16 arctan(1/5) - 4 arctan(1/239)

where are present the numbers 5 and 239 (and 761, as a sort of "phantasm"...).

8) Now some others numeric curiosities:
a) The values of the exponential constant e elevated to Pi is 23.1407. We can get it by the numbers 761 and 239, with only an error of 1/10 000.

3rd Formula


b) 239 and 23 are the only numbers that cannot be represented in fewer than 9 positive cubes.
Note that 239 = 10 x 23 + 9.

c) The sum of the squares of the 7 first prime numbers is 666. Playing with these numbers we obtain: 666/7 - 1/7 + 666 = 761.

d) The first 144 decimals of Pi sum 666.
Then we can see that: 666 - 144 = 761 - 239 = 522 = 2 x 261 (V/ paragraph 10)
And: 522 - 434 = 88, the perimeter of the Great Pyramid’s base.

e) Playing with the numbers of the 3 isosceles triangles:

4th Formula

Then: 761 - 317 = 444; 761 - 477 = 284; 761 - 533 =228
and: 444 + 284 + 228 = 956 = 4 x 239.

f) A good approximation to Pi:

5th Formula

with practically 9 decimals correct.

9) As promised in "First communication", next I give the 55 + 1 pairs of numbers that have digital root of 5 and sum 1000. Of these, 9 pairs are formed by prime numbers (V/ paragraph 2 in "First communication"):
    Posição A B
    1 995 5
    2 986 14
    3 977 23
    4 968 32
    5 959 41
    6 950 50
    7 941 59
    8 932 68
    9 923 77
    10 914 86
    11 905 95
    12 896 104
    13 887 113
    14 878 122
    15 869 131
    16 860 140
    17 851 149
    18 842 158
    19 833 167
    20 824 176
    21 815 185
    22 806 194
    23 797 203
    24 788 212
    25 779 221
    26 770 230
    27 761 239
    28 752 248
    29 743 257
    30 734 266
    31 725 275
    32 716 284
    33 707 293
    34 698 302
    35 689 311
    36 680 320
    37 671 329
    38 662 338
    39 653 347
    40 644 356
    41 635 365
    42 626 374
    43 617 383
    44 608 392
    45 599 401
    46 590 410
    47 581 419
    48 572 428
    49 563 437
    50 554 446
    51 545 455
    52 536 464
    53 527 473
    54 518 482
    55 509 491
    (56) (500) (500)
Only the pair 761-239 solves the equation presented in that paragraph.

10) In the list above are marked the pairs of prime numbers. The sum of their positions is 261.
And: 261 = ( 761 - 239 ) /2.
The last pair, 500 - 500, gives us, when juxtaposed, 500500, that is the triangular number of 1000.

11) At least and still about the number 5761, I advert you to a curious coincidence with the History of religions (already mentioned in my article published in the revue "Colóquio-Artes" nr. 85, June 90, edited by Calouste Gulbenkian Foundation, Lisbon): according to the hebraic sacred chronology, the date of the creation of the Universe (Anno Mundi) is 3761 B.C. So, the year 5761 of that chronology (from September.2000 to September.2001) coincide with the transition from the Second to the Third Millenium.
(note: in the Michael Drosnin's The Bible Code, 97, the author decode the preceding year, 5760 (from September.1999 to September.2000); so, coincident with the end of the Second Millenium. In the context of his investigation, to that year is attributed an apocalyptic sense, like we can found in Nostradamus).

Coincidences... coincidences...
Too much coincidences...




Carlos Calvet
Lisbon, December 1997

On Pi, see: v/ David Blatner <http://www.joyofpi.com/>

 

http://carloscalvet.planetaclix.pt

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