Walter Schauberger, based on the acoustic law, discovered the hyperbolic cone. This is the hyperbolic function rotated around the Y-axis representing the three dimensional acoustic law.

On this hyperbolic cone you can create a hyperbolic spiral when the rate of curvature and climbing are equal. Looking from the top of the spiral downwards you get this figure, which is the same of a water vortex or a spiral galaxy:

If we cut the hyperbolic cone with a plane on different highs Z0 in combination with different cutting angles (alpha, cutting angle) we obtain all possible egg-curves with different size and shape (big, small, long or short).

The german astronomic researcher Johannes Kepler discovered the 3 famous law's describing planets movements around the sun studying the harmony in acoustics. In his opera Astronomia nova " physica coelestis " de motibus stellae MARTIS from the year 1609 Kepler wrote: "The trajectory of a planet is not a circle but it has the shape of an egg." and "we can show, that the trajectory is really an egg-curve and not elliptical". This means that the hyperbolic cone or the three dimensional acoustic law contains the laws of planets movements and he represent an universal law of nature. Kepler used the elliptic equations only for simplifying the calculations obtaining an approximation telling everybody that in reality planets are following egg-curves. Today most scientist think, that planets move on elliptic curves even if its well know, that the gravitational potential of the sun is hyperbolic.

Besides the acoustic law, there's another universal law that itself is manifested in the music notes too: The golden section.

The harmonic proportions in music goes with the Fibonacci-series (1, 1, 2, 3, 5, 8, 13, 21, 34, ...), where every number is the sum of the two numbers before in the series. Dividing a number by its number before, we obtain the irrational number of the golden section increase in precision using higher numbers: Phi = 1,618034... The number 1,618034... >0,618 ~ (PI/4)^2. is the only one for which we can affirm:

1,618 = 1/0,618 = 1,618 plus 1 and

1,6182 = 2,618 and

0,618 ~ (PI / 4)2

Another representation of Phi is an infinite fraction based exclusively on the number 1.

If the hyperbolic cones and the golden section represent universal laws of nature, may-be they is a relationship between them ? Yes there is a common base and we will demonstrate it. For this purpose we have to cut the hyperbolic cone in a way, that we obtain an egg with a golden section i.e. that is 1,618034 times longer than width. For the calculation of the egg-coordinates we use the parametric equation of Prof. Norbert Harthun and Prof. Ines Rennert:

By an iteration method we can find out, that only the cutting angle of 51,84” and high Z0 = 7,65 is good to get the egg with golden proportions. Varying the cutting angle or high, the value diverge fastly from Phi =1,618034... The golden egg has a length of 0,423584 units and a width of 0,261789 units, the volume is 0,009408 volume-units.

We were searching for the relationship between the hyperbolic law and the golden section. For this purpose we will study the geometry of the Cheops-Pyramid.

If we divide the length of the 4 borders around the quadratic base by (d) PI=3,14 we get the height of this pyramid. The angle between the side-triangles and the base is 51,84”. If you draw a line between pyramids top to the mid of one of the 4 borders, the length of this line is 1,618034 times longer than the line from the center of the quadratic base to the mid of a side borderline. This means that the hyperbolic cone give us the golden section using the pyramid angle of 51,84” for the inclination of the cutting plane. For this reason, the angle of 51,84” is the golden angle.

Another analogy come from the water molecule examined intensively by Viktor and Walter Schauberger. The shape of the water-molecule is V-like and symmetric. The angle between the two hydrogen-atoms is ca. 104”, this means ca. 52” from middle-axis, very close to the golden angle. Viktor Schauberger said, that the energy of a single water-drop is equal to the power output of an average electrical-power station. In addition to this he said, that we have to understand copy nature for getting this natural energy for free. Nature is telling us its secret by harmonic laws (hyperbolic cone, golden section). I think, that Neutrinopower, Chi, Prana, live-force, Orgone-Energy, time-emanation, nervous ether, gravitation etc. have the same origin like the pyramid-energy that manifest the same universal law like the planets that are following egg-curves on the hyperbolic cone which is the law of music. Somebody said, that the universe is singing.

Dipl. Ing. Christian Lange, June 2002

Thanks to: Jšrg Schauberger, Prof. Norbert Harthun, Prof. Ines Rennert, Claus Radlberger, Klaus Rauber and my friend Arturo Rinaldi, that gave me the idea to calculate an egg with the golden section.

Sources: www.pks.or.at, "The hyperbolic cone" from Claus Radlberger (in german).

Christian

99.64.11 Response from a Jewish mathematician (Jerryiuliano) 

From: Jerryiuliano@aol.com
To: MetPhys@aol.com
Subject: Response from a Jewish mathematician (Jerryiuliano) 
Date: 07/28/02

Jerry Iuliano discovered several almost identities related to the weak force constant a(em)=137.03599976. Some of these identities are dependent or constitute purely mathematical almost identities. Here is the list of them.

(1) 2882/p/100=cos a(em)  (relative error 3x10-6)

(2) 102/p/.37=a(em)1/2  (relative error 1.6x10-6)

(3) 10144/37/37/18= a(em)1/2  (relative error 7.5x10-7) Indentities (2) and (3) imply the mathematical identity

(3a) 1070/37-2/p=18  (relative error 8.8x10-7)

Thus (2) is rather the result of (3) and (3a). Iuliano then brings different versions of (3) with exponents like 1260/666 etc.with different ŅdreamÓ numbers. They follow from the fact that these ŅdreamÓ numbers are the same mod 37, namely

33=70=144=2808=9505 mod 37.

(4) (180/p)2/px37/100/57= a(em)-1/2  (relative error 3.8x10-7)
Note that (180/p)2/p is nearly a ŅniceÓ rational number.

(5) (180/p)2/p=13+(2/5)2 =14x(37+57)/100 (relative error 6x10-7) Indentities (2) and (4) imply

(4a) (10x180/p)2/p=57  (relative error 1.2x10-6)
Hence (2) is rather consequence of (4) and (4a). By (5) and (4a)

(4b) 102/p =57/13.16=57x100/14/(37+57)  (relative error 1.9x10-6)
From (4b) and (2) follows a nice rational approximation of

(4c) a(em)1/2 =57x100/14/(37+57)/.37  (relative error 2.2x10-7)

(5a) (180/p)2/p/(.37+.57)=14 is identical to (5)

(6) e(p+8)/2 (1/37+1/57)= a(em)1/2  (relative error 1x10-7) By (6) and (4c)

(6a) e(p+8)/2 = (100x57/(37+57))2 /14  (relative error 3.1x10-7)

Other identities that involve e(p+8)/2 follow from (6) and the previous identities. Iuliano also brings identity related to the Feigenbaum constant.

(7) tan-1 ((cos a(em))-p)+p=4.669201609  (relative error 6.7x10-7) Iuliano then mistakenly identifies tan-1 with cot instead of arctan. Identity (7) has no geometric meaning. But by (1)

(7a) tan-1 ((cos a(em))-p)=tan-1 (102p/2882) which is the angle of right triangle with sides 102p and 2882.

The fact that the ratio of the height of the great pyramid to its base is 2/p , is well known. It does not mean however that the builders of the pyramid new the above identities. The number p represents the ratio of female (round) to men (straight). This relation could be demonstrated in the approximation 355/113=p (relative error 8.5x10-8). 355 is the numerical value of xŠ (year), (also the number of days in a regular lunar year is 354-355 days); 113 is the numerical value of ™“‰ PeLeG(part or half). Year symbolizes a periodicity of the circle while the diameter divides it into two equal parts.

The volume of the covering of the arc was 15x9x1=135 palms. From it two keruvim were beaten out, a boy and a girl. Their wings were forming an arc above the straight covering, split my infinitesimal gap. If you take the number 135, double it (as to make two keruvim) as 11 33 55, separate them into two bodies 113 355, and take the ratio 355/113 you obtain the number p. The same idea was presented in the size of womenÕs and menÕs courts in the Temple. The first one was 135 by 135 cubits, the second one 135 by 187.

Why such strange dimensions? The size of the court in the desert was 50 by 100 cubits. In the Temple the sizes were doubled. So one would expect the menÕs court to be 100 by 200 and the womenÕs 100 by 100. Instead it was 135. This number was doubled in the middle 13 35. 35 was add to 100 and 13 subtracted from 200. The number 10 represents creation (the world was created by 10 sayings of G-d) or the basic unit of multitude, while 2/p the relation of masculine to feminine. Thus 102/p may have the meaning of creation and multiplication through coupling. The square of it 104/p may have a similar meaning since 4/p is the ratio of the perimeter of square to the one of the inscribed circle, i.e. masculine to feminine. The number 137 is the numerical value of և“Š (Kaballa).

This is also the number of years of life of Ishmael, Levy and Amram and the age of Abraham when G-d told him to offer Yizhaq as burnt offering. 37 is the age of Yizhaq when he was offered as burnt offering (he was than "reborn"). The number 0.37=37/100 is the ratio of the said age of Yizhaq and the age of Abraham when Yizhaq was born. Identity (2) than may be rewritten as (2*) 104/p = (37/100)2x137 and could interpreted as a linkage between the creation of the world and the burnt offering of Yizhaq by Abraham ( I donÕt know the reason why some numbers are squared and some not). The exact age of Abraham at that moment could have been close to 137.036 years. According to my calculation this was Nissan 18, year 2086 (1675 b.c.), 3 days after G-d talked to Abraham on the 37-th birth-day of Yizhaq . The sunrise of this day was 13.25 days after the vernal equinox (calculated according to the rules of Hebrew calendar). Abraham was born on Nissan of 1949. If he was born at the moment of vernal equinox then at the time of the burnt offering he was 137.03628 years old. If we replace 137 in (2*) by 137.03628, than the indentity holds with relative error of 1.3x10-6, i.e. better than (2)! Identity (1) could be rewritten as (1*) 2882/p =100x cos 137

The number 2882/p may have the same meaning as 102/p , namely creation but in the heavenly sphere. The right hand side has the following geometrical meaning. This is the real part of a complex vector of the length 100 rotated by the angle of 137 rad. Again 100 is the age of Abraham when Yizhaq was born and 137 is his age at the burnt offering. If we replace 137 by 137.03628, the identity holds with relative error of 7x10-4. The reason for the increase in error is that the angle 137 rad is very large, while cos is effected only by the remainder of it mod (2p). Identity (3) should be rewritten as

(3*) 10288/37 = (37x18)2 x137.

The number 18 is the numerical value of Ž (live), thus 37x18 means Yizhaq lived 37 years. The number 288/37 is the ratio of Malkut to the age of Yizhaq. Identity (3a) becomes (3a*) 1070/37=18x102/p

The number 70 is the standard length of life, this was the number of years given to David. The ratio 70/37 relates this age to the age of Yizhaq, 18-live, 102/p multitude. Identity (4) becomes (4*) (180/p)2/p =57x(100/37)/137-1/2

The ratio 180/p is one radian. The circle is divided into 360 degrees similarly to the division of the year into days. The circumference of the circle is 2p. The number 180/p is the ratio of time to distance. On the right-hand side 100/37 is the ratio of the age of Abraham when Yizhaq was born to the age of Yizhaq when he was ŅrebornÓ. The number 57 is the numerical value of ”¾‡ (altar) ((”=40, ¾=7, ‡=2, =8. The whole essence of the burnt offering of Yizhaq, is that he was raised to the altar. Thus the r.h.s. of (4*) is entirely related to this event. Now we understand why the numbers 37 and 57 are paired together in the identities (4)-(6a). The number 13 in the r.h.s. of (5) means bond or unity (the numerical value of ˆ‹ (one) is 13). The number (2/5)2=202/502 is the ratio of the area of the Holy of Holies in the Temple to the area of the front yard in the desert. The number 14 in (4b),(4c),(5a) and (6a ) stands for the day of Passover, Nissan 14. This is the day when Yizhaq was born (actually Yizhaq was born on Nissan 15. However, due to the uncertainty in the definition of the first day of the month, this day could be called also Nisan 14). The exponent e(p+8)/2 has apparently the same meaning as 10(p+8)/2 = 10p/2x1002.

Of course, the above interpretations are merely guesses. The skeptic would say that Iuliano "cooked" up these identities by playing with many free parameters. With computer on hand one could easily check 106 points in the parameter space and obtain accuracy of order 10-6. Suppose that Iuliano wants to find an identity of the type (2) or (4b)

(8*) 102/p = 37a100ba(em)c57d(37+57)e18f14g

where a =1,0,-1, b=2,1,0,-1,-2, c=1,1/2,0,-1/2,-1, d,e,f,g three choices each one as in a. The total number of parameters is 6075. The log of the r.h.s. of (8*) has a distribution close to a normal with average 0 and standard deviation s= 8.7. The log of the l.h.s. of (8*) is 0.64, close to zero. The density of the normal distribution there is about (2ps2)-1/2=0.046. The probability to get close to it as 10-6 in 6075 trials is about 5.6x10-4. If we allow at the l.h.s. of (8*) the exponent 2ipj with i=2,1,0,-1,-2, j=1,-1 the probability increases to 5.6x10-3.

Yet one should acknowledge that identities (1),(2),(4),(5) have the same exponent 2/p and they include not 7 factors as in (8*) but 3 in (2), 4 in (4b) and 4 in (4). Thus one should leave for (2) at least the above improbability 5.6x10-4 . Since the error in (2) is 1.6x10-6 , the improbability of (2) is actually 9x10-4 and similarly for (4b) 10.7x10-4. The combined improbability of (2) and (4b) is about 10-6. The improbability of (4) with the given l.h.s. is 2.1x10-4. Identity (5) follows from (4) and (4c). The latter follows from (2) and (4b). Identity (1) has a special term cos a(em) at the r.h.s., (3) has a special exponent, (6) has an additional term 8 in the exponent, (7) does not fit in any framework. My conclusion is that the identities of Iuliano are indeed a sign of divine supervision. May be one will find in the future a more general framework for it.