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REPRODUCCION DE LOS CONEJOS EN FUNCION A LA SERIE DE FIBONACCI, INCLUSO DEL RELOJ Y DE LA MISMA SANTA CENA (MISMA MANZANA)
 
Apocalipsis 21
1. Vi un cielo nuevo y una tierra nueva; porque el primer cielo y la primera tierra pasaron, y el mar ya no existía más.
2. Y yo Juan vi la santa ciudad, la nueva Jerusalén, descender del cielo, de Dios, dispuesta como una esposa ataviada para su marido.
3. Y oí una gran voz del cielo que decía: He aquí el tabernáculo de Dios con los hombres, y él morará con ellos; y ellos serán su pueblo, y Dios mismo estará con ellos como su Dios.
4. Enjugará Dios toda lágrima de los ojos de ellos; y ya no habrá muerte, ni habrá más llanto, ni clamor, ni dolor; porque las primeras cosas pasaron.
5. Y el que estaba sentado en el trono dijo: He aquí, yo hago nuevas todas las cosas. Y me dijo: Escribe; porque estas palabras son fieles y verdaderas.
6. Y me dijo: Hecho está. Yo soy el Alfa y la Omega, el principio y el fin. Al que tuviere sed, yo le daré gratuitamente de la fuente del agua de la vida. (911 O SALMO 119)
7. El que venciere heredará todas las cosas, y yo seré su Dios, y él será mi hijo.
8. Pero los cobardes e incrédulos, los abominables y homicidas, los fornicarios y hechiceros, los idólatras y todos los mentirosos tendrán su parte en el lago que arde con fuego y azufre, que es la muerte segunda.
9. Vino entonces a mí uno de los siete ángeles que tenían las siete copas llenas de las siete plagas postreras, y habló conmigo, diciendo: Ven acá, yo te mostraré la desposada, la esposa del Cordero.
10. Y me llevó en el Espíritu a un monte grande y alto, y me mostró la gran ciudad santa de Jerusalén, que descendía del cielo, de Dios,
11. teniendo la gloria de Dios. Y su fulgor era semejante al de una piedra preciosísima, como piedra de jaspe, diáfana como el cristal.
12. Tenía un muro grande y alto con doce puertas; y en las puertas, doce ángeles, y nombres inscritos, que son los de las doce tribus de los hijos de Israel; (EL MISMO RELOJ, O SANTA CENA O LA MANZANA, LA TRASLACION EN EL TIEMPO)
13. al oriente tres puertas; al norte tres puertas; al sur tres puertas; al occidente tres puertas.
14. Y el muro de la ciudad tenía doce cimientos, y sobre ellos los doce nombres de los doce apóstoles del Cordero.
15. El que hablaba conmigo tenía una caña de medir, de oro, para medir la ciudad, sus puertas y su muro.
16. La ciudad se halla establecida en cuadro, y su longitud es igual a su anchura; y él midió la ciudad con la caña, doce mil estadios; la longitud, la altura y la anchura de ella son iguales. (CUBO=ESPACIO/TIEMPO)
17. Y midió su muro, ciento cuarenta y cuatro codos, de medida de hombre, la cual es de ángel. (EL NEXO DE LA MANZANA, EL PENTAGONO, LA NUEVA JERUSALEN, EL CASTILLO SAN ANGELO DEL VATICANO E INCLUSO EL MISMO PENTAGONO DE WASHINGTON D.C. ES OBVIO EL NEXO DEL RELOJ CON LA MANZANA)
18. El material de su muro era de jaspe; pero la ciudad era de oro puro, semejante al vidrio limpio;
19. y los cimientos del muro de la ciudad estaban adornados con toda piedra preciosa. El primer cimiento era jaspe; el segundo, zafiro; el tercero, ágata; el cuarto, esmeralda;
20. el quinto, ónice; el sexto, cornalina; el séptimo, crisólito; el octavo, berilo; el noveno, topacio; el décimo, crisopraso; el undécimo, jacinto; el duodécimo, amatista.
21. Las doce puertas eran doce perlas; cada una de las puertas era una perla. Y la calle de la ciudad era de oro puro, transparente como vidrio.
22. Y no vi en ella templo; porque el Señor Dios Todopoderoso es el templo de ella, y el Cordero.
23. La ciudad no tiene necesidad de sol ni de luna que brillen en ella; porque la gloria de Dios la ilumina, y el Cordero es su lumbrera. (PROVERBIOS 25:11, OSEA LA MISMA MANZANA, OSEA UNA REFERENCIA AL SOL/ORO/HOMBRE Y LUNA/PLATA/MUJER, OSEA EL MISMO SUEÑO DE JOSE DE GENESIS 37)
24. Y las naciones que hubieren sido salvas andarán a la luz de ella; y los reyes de la tierra traerán su gloria y honor a ella.
25. Sus puertas nunca serán cerradas de día, pues allí no habrá noche.
26. Y llevarán la gloria y la honra de las naciones a ella.
27. No entrará en ella ninguna cosa inmunda, o que hace abominación y mentira, sino solamente los que están inscritos en el libro de la vida del Cordero.
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Soul, Body and Spirit http://www.spirasolaris.ca/solexp3.html The ALCHEMICAL Aspect
Quote:
In light of the above there seems little doubt that in general and in the present astronomical context in particular, Spira Solaris qualifies to be described numerically as "the One and the Many," the "One and the All," "the Alpha and the Omega," and also (from The Chaldean Oracles): "Fountain of Fountains, and of All Fountains,
The Matrix of all Things."
.....
Pythagoras said the sacred Tetractys is: ` the spring having the roots of ever-flowing nature.' .... The four parts of the Decad, this perfect number, are called number, monad, power and cube. And the interweavings and minglings of these in the origin of growth are what naturally completes nascent number; for when a power of a power; and a cube is multiplied on a cube, it is the power of a cube; and when a cube is multiplied on a cube, the cube of a cube; thus all numbers, from which arise the genesis of what arises, are seven: number, monad, power, cube, power of a power, power of a cube, and cube of a cube.
.....
We have seen that the whole nature of things, all the essential properties of physis, were believed by the Pythagoreans to be contained in the tetractys of the decad; and it now appears that, just as we should expect, this ' fountain of ever-flowing nature' contains the periodic movement of life, evolving out of unity and reverting to unity again, in the recurrent revolution of a wheel of birth. It embodies the fundamental Dionysiac representation of palingenesia.
But there is something more in it than this. Pythagoras inherited the music of Orpheus, as well as the reincarnation doctrine of Dionysus. From the Orphics he inherited also the doctrine of the fall of the soul from its first perfect state of union with the divine, its degradation into the darkness of this life and of the underworld, and its final restoration to peace and unity. Now, on the model of this doctrine of the fall of the soul, the Pythagorean philosophy must hold that all existence proceeds out of the One and returns to it again; and that the One alone is perfect, while the manifold world of visible body is a turbid medium of appearance, in which the one truth is half-revealed and half-concealed, as the divine soul is manifest in the flesh and yet obscured by it and degraded.
There is thus, inherent in the representation handed down from Orphism to Pythagoras, not only the primitive wheel of birth, but another aspect of the movement of life, which is best described as a processional movement out of unity into plurality, out of light into darkness. This movement, also, must be revealed in the nature of numbers, and contained in the tetractys. Pythagoras found it in the procession of numerical series, the study of which he originated, thereby rounding the science of number. It is practically certain, also, that in music he discovered the ratios of the octave, the fifth, and the fourth, contained in the harmonic proportion 12: 8: 6. Now a progression like those contained in the tetractys of Plato's worldsoul --the series, 1: 2: 4: 8, 1: 3: 9: 27– is what the Pythagoreans called an harmonia; it is a continuous entity knit together by a principle of unity running through it, namely the logos or ratio (1/2 or 1/3) which links every term to its predecessor by the same bond. Both series, moreover, radiate from the One, which in Pythagorean arithmetic was not itself a number, but the source in which the whole nature of all numbers was gathered up and implicit. When we note, further, that every number is not only a many, but also one number, we can see how Pythagoras would find the whole movement of cosmic evolution contained in the procession of series, in which the One passes out of itself into a manifold, yet without losing all its unity, and a return from the many to the One is secured by that bond of proportion which runs, backwards and forwards, through the whole series and links it into a ' harmony.' It is thus that we must understand the doctrine that ' the whole Heaven is harmony and number.' The processional movement of physis is modelled upon that of soul, which falls from its first state of union with the divine, but yet remains linked to the One life by mysterious bonds, and can return to it again, purified by music.
......
As for the "geometric figure", that we may already have (whether applicable here or not) and although the concept of "organic motion" may strike some modern readers as strange, it is nevertheless an underlying feature in many ancient major works--the Timaeus of Plato especially. Here it may also be observed that by expressing the exponents of this short section of the Phi-series planetary framework in thirds, the sets [3, 6, 9 , [4, 8, 12] and [6, 12, 18] are also apparent--sets that may or may not be considered further with respect to other passages in Plato, etc.
......
It is in the same fashion that the Timaeus also tries to give a physical account of how the soul moves its body; the soul, it is there said, is in movement, and so owing to their mutual implication moves the body also. After compounding the soul-substance out of the elements and dividing it in accordance with the harmonic numbers, in order that it may possess a connate sensibility for 'harmony' and that the whole may move in movements well attuned, the Demiurge bent the straight line into a circle; this single circle he divided into two circles united at two common points; one of these he subdivided into seven circles. All this implies that the movements of the soul are identified with the local movements of the heavens. (Aristotle, On the Soul)
......
Mind is the monad, science or knowledge the dyad (because it goes undeviatingly from one point to another), opinion the number of the plane, sensation the number of the solid; the numbers are by him expressly identified with the Forms themselves or principles, and are formed out of the elements; now things are apprehended either by mind or science or opinion or sensation, and these same numbers are the Forms of things. Some thinkers, accepting both premises, viz. that the soul is both originative of movement and cognitive, have compounded it of both and declared the soul to be a self-moving number. (Aristotle, On the Soul)
......
Thus that in the soul which is called mind (by mind I mean that whereby the soul thinks and judges) is, before it thinks, not actually any real thing. For this reason it cannot reasonably be regarded as blended with the body: if so, it would acquire some quality, e.g. warmth or cold, or even have an organ like the sensitive faculty: as it is, it has none. It was a good idea to call the soul 'the place of forms', though (1) this description holds only of the intellective soul, and (2) even this is the forms only potentially, not actually. (Aristotle, On the Soul)
.....
there will be a need for several sciences. The first and most important of them is likewise that which treats of pure numbers--not numbers concreted in bodies, but the whole generation of the series of odd and even, and the effects which it contributes to the nature of things. When all this has been mastered, next in order comes what is called by the very ludicrous name mensuration, but is really a manifest assimilation to one another of numbers which are naturally dissimilar, effected by reference to areas. Now to a man who can comprehend this, it will be plain that this is no mere feat of human skill, but a miracle of God's contrivance. Next, numbers raised to the third power and thus presenting an analogy with three-dimensional things. Here again he assimilates the dissimilar by a second science, which those who hit on the discovery have named stereometry [the gauging of solids], a device of God's contriving which breeds amazement in those who fix their gaze on it and consider how universal nature molds form and type by the constant revolution of potency and its converse about the double in the various progressions. The first example of this ratio of the double in the advancing number series is that of 1 to 2; double of this is the ratio of their second powers [ 4 ], and double of this again the advance to the solid and tangible, as we proceed from 1 to 8 [ 1, 2, 2^2, 2^3]; the advance to a mean of the double, that mean which is equidistant from lesser and greater term [the arithmetical], or the other mean [the harmonic] which exceeds the one term and is itself exceeded by the other by the same fraction of the respective terms--these ratios of 3 : 2 and 4 : 3 will be found as means between 6 and 2: why, in the potency of the mean between these terms [ 6 x 2 ], with its double sense, we have a gift from the blessed choir of the Muses to which mankind owes the boon of the play of consonance and measure, with all they contribute to rhythm and melody.
So much, then, for our program as a whole. But to crown it all, we must go on to the generation of things divine, the fairest and most heavenly spectacle God has vouchsafed to the eye of man. And: believe me, no man will ever behold that spectacle without the studies we have described, and so be able to boast that he has won it by an easy route. Moreover, in all our sessions for study we are to relate the single fact to its species; there are questions to be asked and erroneous theses to be refuted. We may truly say that this is ever the prime test, and the best a man can have; as for tests that profess to be such but are not, there is no labor so fruitlessly thrown away as that spent on them. We must also grasp the accuracy of the periodic times and the precision with which they complete the various celestial motions, and this is where a believer in our doctrine that soul is both older and more divine than body will appreciate the beauty and justice of the saying that ' all things are full of gods ' and that we have never been left unheeded by the forgetfulness or carelessness of the higher powers. There is one observation to be made about all such matters. If a man grasps the several questions aright, the benefit accruing to him who thus learns his lesson in the proper way is great indeed; if he cannot, 'twill ever be the better course to call on God. Now the proper way is this--so much explanation is unavoidable. To the man who pursues his studies in the proper way, all geometric constructions, all systems of numbers, all duly constituted melodic progressions, the single ordered scheme of all celestial revolutions, should disclose themselves, and disclose themselves they will, if, as I say, a man pursues his studies aright with his mind's eye fixed on their single end. As such a man reflects, he will receive the revelation of a single bond of natural interconnection between all these problems. If such matters are handled in any other spirit, a man, as I am saying, will need to invoke his luck. We may rest assured that without these qualifications the happy will not make their appearance in any society; this is the method, this the pabulum, these the studies demanded; hard or easy, this is the road we must tread. (The Collected Dialogues of Plato)
http://www.spirasolaris.ca/sbb4d.html |
1998 + ONEneo = 1999 http://en.wikipedia.org/wiki/The_Matrix http://en.wikipedia.org/wiki/Aztec_calendar_stonehttp://en.wikipedia.org/wiki/Theory_of_relativityhttp://en.wikipedia.org/wiki/Magic_squarehttp://en.wikipedia.org/wiki/Sierpinski_trianglehttp://www.davidicke.com/forum/showt...=61370&page=73 http://www.spirasolaris.ca/sbb4d2c.html http://www.banksy.co.uk/http://edition.cnn.com/2013/10/28/us...ter-editorial/  http://www.davidicke.com/forum/showp...postcount=1449
__________________
CRISTIS
Last edited by science2art; 02-11-2013 at 05:54 PM. Reason: Thatcheria mirabilis Spiral/911 "betrayal"
https://forum.davidicke.com/showthread.php?p=1061814088 |
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Soul, Body and Spirithttp://www.spirasolaris.ca/solexp3.htmlThe ALCHEMICAL Aspect
Quote:
In light of the above there seems little doubt that in general and in the present astronomical context in particular, Spira Solaris qualifies to be described numerically as "the One and the Many," the "One and the All," "the Alpha and the Omega," and also (from The Chaldean Oracles): "Fountain of Fountains, and of All Fountains,
The Matrix of all Things."
.....
Pythagoras said the sacred Tetractys is: ` the spring having the roots of ever-flowing nature.' .... The four parts of the Decad, this perfect number, are called number, monad, power and cube. And the interweavings and minglings of these in the origin of growth are what naturally completes nascent number; for when a power of a power; and a cube is multiplied on a cube, it is the power of a cube; and when a cube is multiplied on a cube, the cube of a cube; thus all numbers, from which arise the genesis of what arises, are seven: number, monad, power, cube, power of a power, power of a cube, and cube of a cube.
.....
We have seen that the whole nature of things, all the essential properties of physis, were believed by the Pythagoreans to be contained in the tetractys of the decad; and it now appears that, just as we should expect, this ' fountain of ever-flowing nature' contains the periodic movement of life, evolving out of unity and reverting to unity again, in the recurrent revolution of a wheel of birth. It embodies the fundamental Dionysiac representation of palingenesia.
But there is something more in it than this. Pythagoras inherited the music of Orpheus, as well as the reincarnation doctrine of Dionysus. From the Orphics he inherited also the doctrine of the fall of the soul from its first perfect state of union with the divine, its degradation into the darkness of this life and of the underworld, and its final restoration to peace and unity. Now, on the model of this doctrine of the fall of the soul, the Pythagorean philosophy must hold that all existence proceeds out of the One and returns to it again; and that the One alone is perfect, while the manifold world of visible body is a turbid medium of appearance, in which the one truth is half-revealed and half-concealed, as the divine soul is manifest in the flesh and yet obscured by it and degraded.
There is thus, inherent in the representation handed down from Orphism to Pythagoras, not only the primitive wheel of birth, but another aspect of the movement of life, which is best described as a processional movement out of unity into plurality, out of light into darkness. This movement, also, must be revealed in the nature of numbers, and contained in the tetractys. Pythagoras found it in the procession of numerical series, the study of which he originated, thereby rounding the science of number. It is practically certain, also, that in music he discovered the ratios of the octave, the fifth, and the fourth, contained in the harmonic proportion 12: 8: 6. Now a progression like those contained in the tetractys of Plato's worldsoul --the series, 1: 2: 4: 8, 1: 3: 9: 27– is what the Pythagoreans called an harmonia; it is a continuous entity knit together by a principle of unity running through it, namely the logos or ratio (1/2 or 1/3) which links every term to its predecessor by the same bond. Both series, moreover, radiate from the One, which in Pythagorean arithmetic was not itself a number, but the source in which the whole nature of all numbers was gathered up and implicit. When we note, further, that every number is not only a many, but also one number, we can see how Pythagoras would find the whole movement of cosmic evolution contained in the procession of series, in which the One passes out of itself into a manifold, yet without losing all its unity, and a return from the many to the One is secured by that bond of proportion which runs, backwards and forwards, through the whole series and links it into a ' harmony.' It is thus that we must understand the doctrine that ' the whole Heaven is harmony and number.' The processional movement of physis is modelled upon that of soul, which falls from its first state of union with the divine, but yet remains linked to the One life by mysterious bonds, and can return to it again, purified by music.
......
As for the "geometric figure", that we may already have (whether applicable here or not) and although the concept of "organic motion" may strike some modern readers as strange, it is nevertheless an underlying feature in many ancient major works--the Timaeus of Plato especially. Here it may also be observed that by expressing the exponents of this short section of the Phi-series planetary framework in thirds, the sets [3, 6, 9 , [4, 8, 12] and [6, 12, 18] are also apparent--sets that may or may not be considered further with respect to other passages in Plato, etc.
......
It is in the same fashion that the Timaeus also tries to give a physical account of how the soul moves its body; the soul, it is there said, is in movement, and so owing to their mutual implication moves the body also. After compounding the soul-substance out of the elements and dividing it in accordance with the harmonic numbers, in order that it may possess a connate sensibility for 'harmony' and that the whole may move in movements well attuned, the Demiurge bent the straight line into a circle; this single circle he divided into two circles united at two common points; one of these he subdivided into seven circles. All this implies that the movements of the soul are identified with the local movements of the heavens. (Aristotle, On the Soul)
......
Mind is the monad, science or knowledge the dyad (because it goes undeviatingly from one point to another), opinion the number of the plane, sensation the number of the solid; the numbers are by him expressly identified with the Forms themselves or principles, and are formed out of the elements; now things are apprehended either by mind or science or opinion or sensation, and these same numbers are the Forms of things. Some thinkers, accepting both premises, viz. that the soul is both originative of movement and cognitive, have compounded it of both and declared the soul to be a self-moving number. (Aristotle, On the Soul)
......
Thus that in the soul which is called mind (by mind I mean that whereby the soul thinks and judges) is, before it thinks, not actually any real thing. For this reason it cannot reasonably be regarded as blended with the body: if so, it would acquire some quality, e.g. warmth or cold, or even have an organ like the sensitive faculty: as it is, it has none. It was a good idea to call the soul 'the place of forms', though (1) this description holds only of the intellective soul, and (2) even this is the forms only potentially, not actually. (Aristotle, On the Soul)
.....
there will be a need for several sciences. The first and most important of them is likewise that which treats of pure numbers--not numbers concreted in bodies, but the whole generation of the series of odd and even, and the effects which it contributes to the nature of things. When all this has been mastered, next in order comes what is called by the very ludicrous name mensuration, but is really a manifest assimilation to one another of numbers which are naturally dissimilar, effected by reference to areas. Now to a man who can comprehend this, it will be plain that this is no mere feat of human skill, but a miracle of God's contrivance. Next, numbers raised to the third power and thus presenting an analogy with three-dimensional things. Here again he assimilates the dissimilar by a second science, which those who hit on the discovery have named stereometry [the gauging of solids], a device of God's contriving which breeds amazement in those who fix their gaze on it and consider how universal nature molds form and type by the constant revolution of potency and its converse about the double in the various progressions. The first example of this ratio of the double in the advancing number series is that of 1 to 2; double of this is the ratio of their second powers [ 4 ], and double of this again the advance to the solid and tangible, as we proceed from 1 to 8 [ 1, 2, 2^2, 2^3]; the advance to a mean of the double, that mean which is equidistant from lesser and greater term [the arithmetical], or the other mean [the harmonic] which exceeds the one term and is itself exceeded by the other by the same fraction of the respective terms--these ratios of 3 : 2 and 4 : 3 will be found as means between 6 and 2: why, in the potency of the mean between these terms [ 6 x 2 ], with its double sense, we have a gift from the blessed choir of the Muses to which mankind owes the boon of the play of consonance and measure, with all they contribute to rhythm and melody.
So much, then, for our program as a whole. But to crown it all, we must go on to the generation of things divine, the fairest and most heavenly spectacle God has vouchsafed to the eye of man. And: believe me, no man will ever behold that spectacle without the studies we have described, and so be able to boast that he has won it by an easy route. Moreover, in all our sessions for study we are to relate the single fact to its species; there are questions to be asked and erroneous theses to be refuted. We may truly say that this is ever the prime test, and the best a man can have; as for tests that profess to be such but are not, there is no labor so fruitlessly thrown away as that spent on them. We must also grasp the accuracy of the periodic times and the precision with which they complete the various celestial motions, and this is where a believer in our doctrine that soul is both older and more divine than body will appreciate the beauty and justice of the saying that ' all things are full of gods ' and that we have never been left unheeded by the forgetfulness or carelessness of the higher powers. There is one observation to be made about all such matters. If a man grasps the several questions aright, the benefit accruing to him who thus learns his lesson in the proper way is great indeed; if he cannot, 'twill ever be the better course to call on God. Now the proper way is this--so much explanation is unavoidable. To the man who pursues his studies in the proper way, all geometric constructions, all systems of numbers, all duly constituted melodic progressions, the single ordered scheme of all celestial revolutions, should disclose themselves, and disclose themselves they will, if, as I say, a man pursues his studies aright with his mind's eye fixed on their single end. As such a man reflects, he will receive the revelation of a single bond of natural interconnection between all these problems. If such matters are handled in any other spirit, a man, as I am saying, will need to invoke his luck. We may rest assured that without these qualifications the happy will not make their appearance in any society; this is the method, this the pabulum, these the studies demanded; hard or easy, this is the road we must tread. (The Collected Dialogues of Plato)
http://www.spirasolaris.ca/sbb4d.html |
1998 + ONEneo = 1999 http://en.wikipedia.org/wiki/The_Matrixhttp://en.wikipedia.org/wiki/Aztec_calendar_stonehttp://en.wikipedia.org/wiki/Theory_of_relativityhttp://en.wikipedia.org/wiki/Magic_squarehttp://en.wikipedia.org/wiki/Sierpinski_trianglehttp://www.davidicke.com/forum/showt...=61370&page=73http://www.spirasolaris.ca/sbb4d2c.htmlhttp://www.banksy.co.uk/http://edition.cnn.com/2013/10/28/us...ter-editorial/http://www.davidicke.com/forum/showp...postcount=1449
__________________
CRISTIS
Last edited by science2art; 02-11-2013 at 05:54 PM. Reason: Thatcheria mirabilis Spiral/911 "betrayal"
https://forum.davidicke.com/showthread.php?p=1061814088 |
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Fibonacci 24 Repeating Pattern
May 15, 2012 by Gary Meisner
The Fibonacci sequence has a pattern that repeats every 24 numbers.
Numeric reduction is a technique used in analysis of numbers in which all the digits of a number are added together until only one digit remains. As an example, the numeric reduction of 256 is 4 because 2+5+6=13 and 1+3=4.
Applying numeric reduction to the Fibonacci series produces an infinite series of 24 repeating digits:
1, 1, 2, 3, 5, 8, 4, 3, 7, 1, 8, 9, 8, 8, 7, 6, 4, 1, 5, 6, 2, 8, 1, 9
If you take the first 12 digits and add them to the second twelve digits and apply numeric reduction to the result, you find that they all have a value of 9.
| 1st 12 numbers |
1 |
1 |
2 |
3 |
5 |
8 |
4 |
3 |
7 |
1 |
8 |
9 |
| 2nd 12 numbers |
8 |
8 |
7 |
6 |
4 |
1 |
5 |
6 |
2 |
8 |
1 |
9 |
| Numeric reduction – Add rows 1 and 2 |
9 |
9 |
9 |
9 |
9 |
9 |
9 |
9 |
9 |
9 |
9 |
18 |
| Final numeric reduction – Add digits of result |
9 |
9 |
9 |
9 |
9 |
9 |
9 |
9 |
9 |
9 |
9 |
9 |
This pattern was contributed both by Joseph Turbeville and then again by a mathematician by the name of Jain.
We would expect a pattern to exist in the Fibonacci series since each number in the series encodes the sum of the previous two. What’s not quite so obvious is why this pattern should repeat every 24 numbers or why the first and last half of the series should all add to 9.
For those of you from the “Show Me” state, this pattern of 24 digits is demonstrated in the numeric reduction of the first 73 numbers of the Fibonacci series, as shown below:
|
Fibonacci Number
|
Numeric reduction by adding digits |
| 1st Level |
2nd Level |
Final Level |
| Example: 2,584 |
2+5+8+4=19 |
1+9=10 |
1+0=1 |
| 0 |
0 |
0 |
0 |
| 1 |
1 |
1 |
1 |
| 1 |
1 |
1 |
1 |
| 2 |
2 |
2 |
2 |
| 3 |
3 |
3 |
3 |
| 5 |
5 |
5 |
5 |
| 8 |
8 |
8 |
8 |
| 13 |
4 |
4 |
4 |
| 21 |
3 |
3 |
3 |
| 34 |
7 |
7 |
7 |
| 55 |
10 |
1 |
1 |
| 89 |
17 |
8 |
8 |
| 144 |
9 |
9 |
9 |
| 233 |
8 |
8 |
8 |
| 377 |
17 |
8 |
8 |
| 610 |
7 |
7 |
7 |
| 987 |
24 |
6 |
6 |
| 1,597 |
22 |
4 |
4 |
| 2,584 |
19 |
10 |
1 |
| 4,181 |
14 |
5 |
5 |
| 6,765 |
24 |
6 |
6 |
| 10,946 |
20 |
2 |
2 |
| 17,711 |
17 |
8 |
8 |
| 28,657 |
28 |
10 |
1 |
| 46,368 |
27 |
9 |
9 |
| 75,025 |
19 |
10 |
1 |
| 121,393 |
19 |
10 |
1 |
| 196,418 |
29 |
11 |
2 |
| 317,811 |
21 |
3 |
3 |
| 514,229 |
23 |
5 |
5 |
| 832,040 |
17 |
8 |
8 |
| 1,346,269 |
31 |
4 |
4 |
| 2,178,309 |
30 |
3 |
3 |
| 3,524,578 |
34 |
7 |
7 |
| 5,702,887 |
37 |
10 |
1 |
| 9,227,465 |
35 |
8 |
8 |
| 14,930,352 |
27 |
9 |
9 |
| 24,157,817 |
35 |
8 |
8 |
| 39,088,169 |
44 |
8 |
8 |
| 63,245,986 |
43 |
7 |
7 |
| 102,334,155 |
24 |
6 |
6 |
| 165,580,141 |
31 |
4 |
4 |
| 267,914,296 |
46 |
10 |
1 |
| 433,494,437 |
41 |
5 |
5 |
| 701,408,733 |
33 |
6 |
6 |
| 1,134,903,170 |
29 |
11 |
2 |
| 1,836,311,903 |
35 |
8 |
8 |
| 2,971,215,073 |
37 |
10 |
1 |
| 4,807,526,976 |
54 |
9 |
9 |
| 7,778,742,049 |
55 |
10 |
1 |
| 12,586,269,025 |
46 |
10 |
1 |
| 20,365,011,074 |
29 |
11 |
2 |
| 32,951,280,099 |
48 |
12 |
3 |
| 53,316,291,173 |
41 |
5 |
5 |
| 86,267,571,272 |
53 |
8 |
8 |
| 139,583,862,445 |
58 |
13 |
4 |
| 225,851,433,717 |
48 |
12 |
3 |
| 365,435,296,162 |
52 |
7 |
7 |
| 591,286,729,879 |
73 |
10 |
1 |
| 956,722,026,041 |
44 |
8 |
8 |
| 1,548,008,755,920 |
54 |
9 |
9 |
| 2,504,730,781,961 |
53 |
8 |
8 |
| 4,052,739,537,881 |
62 |
8 |
8 |
| 6,557,470,319,842 |
61 |
7 |
7 |
| 10,610,209,857,723 |
51 |
6 |
6 |
| 17,167,680,177,565 |
67 |
13 |
4 |
| 27,777,890,035,288 |
73 |
10 |
1 |
| 44,945,570,212,853 |
59 |
14 |
5 |
| 72,723,460,248,141 |
51 |
6 |
6 |
| 117,669,030,460,994 |
65 |
11 |
2 |
| 190,392,490,709,135 |
62 |
8 |
8 |
| 308,061,521,170,129 |
46 |
10 |
1 |
| 498,454,011,879,264 |
72 |
9 |
9 |
Thanks to Joseph Turbeville for sending “A Glimmer of Light from the Eye of a Giant” and to Helga Hertsig for bringing Jain’s discovery of this pattern to my attention.
Filed Under: Math
https://www.goldennumber.net/fibonacci-24-pattern/ |
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Fibonacci Fun
Here are some illustrations by myself and others, dealing with the Fibonacci sequence and the Golden Number, Phi.
A few months ago, I noticed the exponents of Phi encode the Fibonacci sequence.
The sequence gets closer to the golden number the larger the numbers get. This will work with any two starting numbers, like say 91 and 432, for example. You’ll find the same ratio emerge if you keep adding them together. (91+432 = 523, then, 432+523=955, etc) Already we are at 1.8 to 1. (955/523) A handful more steps and we’ll have Phi to more than 99.999% accuracy.
???? If you had a million phalanges, your hand would look like King Midas.
Jain108 made a post on how, if you start with 2 and 10, you arrive at the actual numbers found in the exponents of Phi. Remember exponents are simply the number multiplied by itself n number of times. Phi cubed, or Phi to the third power, is just Phi x Phi x Phi. (1.618 x 1.618 x 1.618 = 4.236) See that was easy, now stop complaining how you’re bad at math.
Phi to the negative power is the same as saying, one divided by the Phi cubed, or whatever.
Here’s some different ways to say the same thing.
This does an excellent job of explaining where all these freaking numbers come from. (img Scott Onstott)
Circles of Fibonacci. Magenta and green cancel out and make gold
Sam Kutler found the golden number in concentric circles.
The outer ring shows the 24 digit pattern(digital roots), the inner the 60 digit pattern(last number).
Lucien Khan rediscovered the 60 digit repeat pattern.
Fibonacci Patterns
Fibonacci sequence hidden in ordinary division problem:
If you divide 1 by 999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999 (that’s 999 quattuordecillion), the Fibonacci sequence pops out.
Chad Adam’s Extended Fibonacci Series
Like I said, you can start a Fibonacci sequence with any two numbers. If you begin with the numbers 1-9, some interesting things happen.
by Chad Adams
See how the numbers match up?
The Platonic Solids
 back to the 60 digit pattern….
The Fibonacci Sequence, starting at the 60th number in the sequence. See the pattern? Just look at the last digit in each number of the sequence. [after 8 is 3 because the last digit in 13(5+8) is 3]
The Colorado State Flag
Is it just me or is Colorado’s state seal illuminaty as all hell?
Don’t even go to Denver International Airport.
I did an article on Decoding the Dollar, and found the leaves on the left side of the buck encode the fib seq. with 2,3,5,8.
The name ‘Fi-Bonacci'(Man of cheer) comes from Leonardo’s old man who could always make the town laugh.
Leonardo de Pisa, the guy we call ‘Fibonacci”, actually had his own value for π, which was 864/275, or 3.141818181818…. (Phi = 1.618..)
I talk about this more here..
The Fibonacci numbers reduced to one digit through digital parity. (21 is 3 because 2+1=3)
This is the number and sequence of numbers that God choose to use to structure all life and creation.
https://joedubs.com/fibonacci-fun/ |
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3 Phi and Triangles
3.1 Phi and the Equilateral Triangle
 Chris and Penny at Regina University's Math Central (Canada) show how we can use any circle to construct on it a hexagon and an equilateral triangle. Joining three pairs of points then reveals a line and its golden section point as follows:
- On any circle (centre O), construct the 6 equally spaced points A, B, C, D, E and F on its circumference without altering your compasses, so they are the same distance apart as the radius of the circle. ABCDEF forms a regular hexagon.
- Choose every other point to make an equilateral triangle ACE.
- On two of the sides of that triangle (AE and AC), mark their mid-points P and Q by joining the centre O to two of the unused points of the hexagon (F and B).
- The line PQ is then extended to meet the circle at point R.
Q is the golden section point of the line PR.
 Q is a gold point of PRThe proof of this is left to you because it is a nice exercise either using coordinate geometry and the equation of the circle and the line PQ to find their point of intersection or else using plane geometry to find the lengths PR and QR.
The diagram on the left has many golden sections and yet contains only equilateral triangles. Can you make your own design based on this principle?
Chris and Penny's page shows how to continue using your compasses to make a pentagon with QR as one side.
- Equilateral Triangles and the Golden ratio J F Rigby, Mathematical Gazette vol 72 (1988), pages 27-30.
http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/phi2DGeomTrig.html |
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