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

 f) A good approximation to Pi: 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/>