Re: Theos-World Plato
Mar 20, 2006 10:36 AM
by Shel Steijl
! I give up
Shel
----- Original Message -----
From: "Cass Silva" <silva_cass@yahoo.com>
To: <theos-talk@yahoogroups.com>
Sent: Monday, March 20, 2006 7:41 AM
Subject: Theos-World Plato
Anyone care to check this site out
http://www.enterprisemission.com/bridge.html
Almost immediately, he discovered something quite astonishing (to a
non-specialist): the surface area of a tetrahedron (the "lowest order,"
simplest Platonic form), inscribed inside a "higher-order" form -- a
sphere-- results in a surface ratio (sphere/tetrahedron) almost precisely
equivalent to "e," the base of natural logarithms:
e = 2.718282
surface of sphere
------------------------------------ = 2.720699
surface of circumscribed tetrahedron
Difference = 0.002417
The derivation of the above is as follows:
(expressions are written in FORTRAN notation)
Let A(t) = surface area of tetrahedron
A(s) = surface area of circumscribing sphere
R = radius of circumscribing sphere
For a regular tetrahedron of edge a:
A(t) = a**2 * sqrt(3) and R = a * sqrt(6)/4
For the circumscribing sphere:
A(s) = 4*pi*R**2 = 4*pi * (a*sqrt(6)/4)**2 = (3/2)*pi*a**2
Area of sphere/area of circumscribed tetrahedron
A(s)/A(t) = (3/2)*pi*a**2/(a**2 * sqrt(3)) = 3*pi/(2*sqrt (3))
A(s)/A(t) = 2.720699 - an approximation of e = 2.718282
When Torun substituted this "close approximation of e", termed e', in
the equation most approximated at Cydonia:
e/pi = 0.865
He discovered that:
e'/pi = 2.720699/3.141593 = 0.866025 = (sqrt 3)/2
Or . . . precisely the observed "e/pi" ratio discovered at Cydonia!
The fact that e'/pi equals (sqrt 3)/2 can be demonstrated
algebraically:
Since e' was defined as 3*pi/(2*sqrt (3)),
e'/pi = 3*pi/(2*sqrt (3)) / pi = 3/(2*sqrt (3)) = sqrt(3)/2
To place the above math in simple terms:
The values of e/pi and (sqrt 3)/2 are
precisely equal when e/pi is evaluated using
the approximation of e that is generated by
the geometry of a circumscribed tetrahedron.
This simple fact completely resolves the ambiguity regarding which
ratio -- e/pi or (sqrt 3)/2 -- was intended at Cydonia (see Fig. 4):
Apparently, both were!
Since the most redundantly observed Cydonia ratio is 0.866 and not
0.865 (the true ratio of the base of natural logarithms, divided by Pi --
to three significant-figures), it must now be clear, however, that the
*primary* meaning of the "geometry of Cydonia" was in all likelihood
intended to memoralize the (sphere)/(circumscribed tetrahedron)
ratio[which is also (sqrt 3/2)], and not "e/pi".
Further examples of "e/pi" at Cydonia -- appearing in connection with
the ArcTan of 50.6 degrees (present at least twice in association with the
Face) -- when examined by Hoagland, confirm that Torun's "circumscribed
tetrahedral ratio" -- e' = 2.72069 -- and NOT the base of natural
logarithms (e = 2.718282) provides a closer fit to the observed number--
Thus strongly implying that "tetrahedral geometry" (and NOT the
usual association of "e" with "growth equations") is the predominent
meaning of "e/(sqrt 5)" and "(sqrt 5)/e" -- two other specific ratios
found redundantly throughout the complex:
e/(sqrt 5) = 1.215652
e'/(sqrt 5) = 1.216734
Cydonia ratio = 1.217 = ArcTan 50.6 degrees
(The detailed implications of this association -- e' and (sqrt 5) --
will be examined in a subsequent paper.)
These results, combined with other examples in the Complex (D&M
Pyramid angles 60 degrees/ 69.4 degrees = 0.865 ) are what lead us to the
conclusion that in fact *both* constants -- e and e' -- are deliberately
encoded at Cydonia. In particular:
D&M Pyramid apex = 40.868 deg N
= ArcTan 0.865256 = e/pi
But another feature on the D&M -- the wedge-shaped projection on the
front -- defines the Pyramid's bilateral symmetry and orientation directly
toward the Face. This feature also now seems to mark an equally important
latitude:
D&M "wedge" = 40.893 deg N
= ArcTan 0.866025 = e'/pi = (sqrt 3)2
Torun identifies a conspicuous "knob," lying at the end of this
wedge, as the "benchmark" designed to mark precisely the correct "e'/pi"
latitude -- 40.893 degrees, approx. 1/40th degree North of the true apex
of the Pyramid. The terminus of this wedge, together with the NW corner of
the pyramid, are the only two points on the pyramid that, when connected,
denote a line of latitude (see Fig. 5).
Again, putting this in simple terms:
The geometry of a circumscribed tetrahedron is not only
suggested by the alignments in Cydonia, but also by the siting
latitude,size, shape, and orientation of the D&M Pyramid itself.
This discovery only underscores the importance apparently attached to
"circumscribed tetrahedral geometry" in the construction of Cydonia --
raising the important question:
Why?
The "Message of Cydonia"
Verification of a highly-specific and redundant communication of
"circumscribed tetrahedral geometry" -- including its obviously
*deliberate* extension to the siting of the Cydonia Complex on the
planet -- would be deemed a phenomenonal discovery. If this is indeed "the
message of Cydonia," crafted by what Mars' hostile environment strongly
implies was a visiting interstellar culture (Hoagland, 1987), then what
could have been its purpose?
Apparently:
To communicate the "importance" of tetrahedral geometry itself!
If this is the successful "decoding of the Message" -- its existence
(if not the sheer effort expended in its communication) must in turn raise
obvious questions regarding "hitherto unrecognized properties" of
circumscribed tetrahedra.
---------------------------------
Yahoo! Mail
Bring photos to life! New PhotoMail makes sharing a breeze.
[Non-text portions of this message have been removed]
Yahoo! Groups Links
--
No virus found in this incoming message.
Checked by AVG Free Edition.
Version: 7.1.385 / Virus Database: 268.2.5/284 - Release Date: 17/03/2006
- References:
- Plato
- From: Cass Silva <silva_cass@yahoo.com>
[Back to Top]
Theosophy World:
Dedicated to the Theosophical Philosophy and its Practical Application
