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From: BARILOCHENSE6999  (Original message) Sent: 08/07/2017 14:24

Ancient cultures knew about sacred geometry reflected in nature and derived their individual measures of length from it. Many ancient writings suggest that this knowledge was given to mankind by god(s). The ‘Gods’ of certain cultures could be early post-flood founders a few generations after Noah. In Egypt, building overseers required the Royal Egyptian Cubit to be calibrated against a precision standard at regular intervals. Failure to do so was punishable by death.  This extreme respect for the royal cubit indicates an important legacy, like a standard handed down from the ‘Gods’.

According to the “Secrets of the Great Pyramid” (by L. Stecchini) the Egyptian measures of length, originating from at least the 3rd millennium BC, were directly derived from the circumference of the earth with an amazing accuracy. On page 346, his claim is that the Egyptian measurement was equal to 40,075,000 meters, which compared to the International Spheroid of 40,076,596 meters gives an error of 0.004%. No consideration seems to be made to the question of, on purely technical and procedural grounds, how the early Egyptians, in defining their cubit, could have achieved a degree of accuracy that to our current knowledge can only be achieved with very sophisticated equipment and techniques.

Note: Egyptians calculated polar radius as 12,000,000 Royal Cubits (of 0.525 m per cubit) which is equivalent of 6300 km (modern value for the polar radius of the  Earth is 6,357km)

The Sacred Cubit (aka Royal Cubit) was used in constructing buildings and monuments and in surveying in ancient Egypt. Royal Cubit consists of 28 units, digits ( 7 palms of 4 digits). The names of divisions of royal cubit may suggest anatomical origin, however the division numbers indicate astronomical origin of the cubit (7 days per week, 28 days lunar calendar, 4 weeks per lunar month)…

Note: Here is an  interesting connection between modern and ancient units of length with astronomy and geodesy:  1 foot = 12 inches1 mile = 5280 feet = 63,360 inches = 4800 Sumerian Feet = 3200 Sumerian Cubits.

There is great confusion today concerning metrology, the history of measurement systems around the world. Beyond the child’s tales of the “foot” deriving from some king’s foot, measurement was actually part of a sacred system of knowledge established in prehistory and based on timeless truths seen in the harmony of the cosmos. Standards of measure were everywhere framed upon never-changing principles of number, in particular, the interplay of natural tension between ten and twelve, and the dimensions of the turning Earth. Except for the survival of the English system in the U.S., most other traditional systems of measurement worldwide have succumbed to the “easy” and modern, but inferior “metric” system, which uses only ten, is divorced from nature and the human scale, and requires its users to conform to the measuring tools themselves, not to the nature of the objects measured, as was traditionally done. 

The Cosmological Diagram (The New Jerusalem Diagram)

The Sacred Geometric Community has fallen short of the grand prize, the New Jerusalem and her fullness of purpose, they have at least seen, especially through the apostolic efforts of John Michell, the suburbs of the Holy City and from this afar view have come imminently close to her profound and universal meaning; and certainly by framing their quests for universal understanding and sustainable social systems in terms of the Celestial City (or as in Plato’s case, Magnesia).  Their approach to the City Whose Builder and Maker is God (even though that “god” is NOT the One of revelation and authority held by their antagonists amongst the aforesaid monotheists), as we all, is seen through a glass darkly but, nevertheless, they are searching to unlock the mystery of the New Jerusalem and to confirm their findings through geodetic discovery.

Another version of the NJ Diagram is Magical Seal of Solomon.

In Medieval Jewish, Christian and Islamic legends, the Seal of Solomon was a magical signet ring said to have been possessed by King Solomon, which variously gave him the power to command demons, genies (or jinni), or to speak with animals. In some versions the seal was made of brass and iron, carved with the Name of God, and set with four jewels. In later versions the ring simply bore the symbol now called the Star of David (hexagram), often within a circle, usually with the two triangles interlaced  rather than intersecting.

To them the “geometric construction” of the New Jerusalem presents cosmological realities which govern the universe – a universe numerically understood far more by the “ancients” who have left us a testament in their objects and writings to these realities whereby John’s vision of the Holy City is the culmination of all their most vivid aspirations; to wit, the elaborate geometric configurations from the New Jerusalem Diagram to intriguing planetary measurements of circles, squares, triangles, polygons of all sorts which provide immediate connectivity between earth and heaven’s realms – as well as those earthly objects of antiquity which replicate the heavenly dimensions of Paradise, and all within the context, preservation and accuracies of antiquity:

“Another relic of the archaic tradition that produced these divisions of time is our present system of measurement by units of feet, furlongs, and miles, with the acre as the unit of land measuring.  Those measures, which are still found the most convenient today, were canonized and held sacred, because not only do they relate both to the human and to the astronomical scales, expressing the unity between macrocosm and microcosm, but they bring out the same numbers in the dimensions of the solar system as were given to the units of time.”  — Dimensions of Paradise, Michell, p. 117.

One of the foremost metrologists of Teotihuacán is, without equivocation, Dr. Hugh Harleston Jr., who during the late 1960s and 1970s measured this “ritual city” from a “…unified geometrical composition whose intervals are clearly defined, and Harleston was soon able to establish the basic unit of measure in its dimensions.  This proved to be a unit of 1.0594 meters, which Harleston called the Standard Teotihuacán Unit (STU) or Hunab after the Mayan word, adopted by the Aztecs, for Measure.  He also recognized the geodetic significance of that unit:  1.0594063 meters is equivalent to the ‘Jewish rod’ of 3.4757485 ft., the same unit which represents the width of the Stonehenge lintels, a six-millionth part of the earth’s polar radius and one part in 37,800,000 of its mean circumference.” (Ref. The New View Over Atlantis, Dr. John Michell, 1995, p. 131).

Also:  “Harleston says of Teotihuacan’s builders: ‘When they draw a line, they’re telling you an area. When they draw an area, they’re telling you a volume.  When they put volume, they’re telling you time.”

Geodesy and geodetic placement of “sacred sites” of ancient origins has long been affirmatively suspect – especially, the Great Pyramid of Giza.  Geodesy involves a fundamental understanding of plane or solid geometry, astronomy relative to latitude and longitude with latitude of more recent vintage since ships-clock (cir. 1540) came into vogue.   These geodetic or geometric relationships both on earth and in the heavens are a frequent haunt of pagans and occultists and of novel interest to science – though science with its unfortunate proliferation of skeptic is apt to go off into “metric tangents” and miss out on all the “fun!”For quite some time researchers have been documenting the astronomical alignments of ancient archaeological and megalithic stone sites all over the world. But discovery of their geodesic alignment has been more recent. Geodesy refers to the theory and practice of surveying to determine the position of specific points on Earth’s surface. It is distinguished from plane surveying in that it deals with areas whose dimensions are so great that the curvature of the Earth must be taken into account. Geometric geodesy involves the creation of a mathematical model of Earth, while physical geodesy studies Earth’s gravity field.  The discovery of the precise alignment of Mayan sites along the 90th parallel is significant because it demonstrates that the Maya were aware of Earth’s curvature and knew the advanced formulas used in geodesy.

Note: Carl Munck, archaeocryptographer, introduces an ancient Pyramid Matrix, in which ancient monuments – across the globe – encode their exact positions with respect to latitude and longitude. The science of decoding these monuments is called archaeocryptography. For latitude, ancient monuments were referenced to the same (modern) equator. For longitude, these monuments were referenced to a former Giza, Egypt Prime Meridian – discovered by Munck – that ran from pole to pole across the Great Pyramid.

PS1  The Forgotten Harmonical Science of the Bible

Note: The following segment is from “The forgotten harmonical science of the Bible” by Ernest G. McClain

“…but thou hast ordered all things in measure and number and weight” — Wisdom of Solomon 11:20  (1611 King James Bible)

Biblical creation “by measure, number and weight”  required God to possess a fluency in arithmetic not always shared by the faithful. And so Bible arithmetic of the first millennium BC eventually became incomprehensible.

Today much of the astronomy, arithmetic, and music attributed to Classical Greece is documented to Semitic Babylon in the second millennium B.C.   Mesopotamian fluency in calculation–in the age of Abraham, Isaac, and Jacob–already was 3000 years ahead of 16th century AD Europe. Babylonian exile in the sixth century BC made accessible to the Jews anything not already known.

With help of Philo of Alexandria I am reading Divine prescience as pre-scientific musical insight encoded in tribal mythology.  Biblical emphasis on twelve sons as eponymous ancestors of twelve tribes who build an altar of twelve stones concerns twelve idealized “boundary markers” in a cyclic octave needed for Davidic musicology. The pattern was long symbolized in the concentric circles of the Babylonian astrolabe, adjusted monthly to correlate the watches with the varying lengths of day and night.  Figure 2 strips all star data from van der Waerden’s reconstruction, and converts his base-60 water-clock weights (for full watches in the outer circle, and half and quarter watches in the inner circles) to base 10 arithmetic.

The astrolabe’s naked geometry and simple arithmetical doubling expose the idealist mind set which guided the evolution of Chaldaean sciences — converted to priestly ritual by Jewish ingenuity. Twelve ideal months of 30 fictitious days were superimposed on the heavens, and the ratio of longest night to shortest day, known to be about 3:2, was computed as 2:1, so that only music offered a “manipulable” example which conformed to these rounded measures.

Concentric circles anticipate Ezekiel’s “wheel in a wheel” as the throne of heaven. Within each circle maxima and minima water clock weights of 2:1 anticipate the ratio of cyclic octaves. But equal weight differences between successive months (reversing at the solstices in months III and IX) had to give way to proportional differences between successive semitones when this geometry was applied to music. Rational tonal    arithmetic, cleverly mimed by Ezekiel, could anticipate this conceptual equality only via a slight but cumulative excess or deficiency, for in a cyclic octave of ratio 1:2 all equal divisions are defined by irrationals. Thus the Holy Land of a spiritual Israel had to be conquered conceptually in intricate warfare between the excess of primordial “giants” (products of 3) and the deficiency of human “weaklings” (products of 5) among rational numbers, and “weaklings” won only with Divine help in circumventing the lack of real number. Bible narrative brilliantly allegorizes every aspect of Diophantine approximation to modern Equal Temperament, and it does so with exhausting respect for numerical detail–making the Bible a priceless repository of tuning lore and its elementary number theory. The “unhewn” stones of Jewish altars are integers, meaning the natural or counting numbers to which harmonical theory normally was restricted, although its calculation demanded great fluency with reciprocal fractions. From the perspective of any reference pitch all integers except 2n necessarily “sinned” by “missing the mark” to some degree because octave doubling imposed, a priori, a universal matrix (“womb”) tied to integral powers of 2. Problems arose immediately with division into 2 equal parts (requiring the square root of 2) and 3 parts (requiring the cube root of 2).

Sensory intuition always fails at some level of arithmetical subtlety where least noticeable differences create a Platonic “no man’s land” of uncertainty. Greek, Jewish, and Chinese cultures are unanimous in accepting the comma of 80:81 as its convenient normative value. It is the difference between a “giant” wholetone of 8:9 (worth 204 cents in modern logarithmic measure) and a “human weakling” of 9:10 (worth only 190). They are approximations to the sixth root of 2 worth 200 cents, the value necessary to divide an octave 1:2 into six equal parts. How Davidic tuning theory reconciles this conflict becomes the central focus of Bible allegory  And in the sixth century BC only God could have solved this problem numerically–although any geometer could map results to his own satisfaction for the astrolabe pointed the way.

For musician/philosophers of Philo’s temperament,  tuning theory may always have been a contest in the soul between the potential tyranny of masculine intellection, considered mankind’s very highest power, and the relative benevolence of our feminine sensorium, where least noticeable differences create some measure of perceptual tolerance. Wisdom required a congenial mating between our own masculine concepts and feminine percepts, and sometimes rewarded it with the experience of transcendent beauty in “out of the body” adventures like Philo enjoyed when listening to the antiphonal singing of segregated sexes in his Alexandrine synagogue. I am trying here to articulate Bible harmonics in Philo’s spirit while paying closer attention to its computational logic.

http://blog.world-mysteries.com/science/the-language-of-god/


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From: BARILOCHENSE6999 Sent: 08/07/2017 16:55
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From: BARILOCHENSE6999 Sent: 15/04/2018 01:38
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COLOSENSES 2:16=216=6*6*6=666 =SISTEMA SEXAGECIMAL=1 DE REYES 10:14= APOCALIPSIS 13:18
2160 MILLAS INGLESAS=DIAMETRO DE LA LUNA
DIAMETRO DE LA TIERRA             (MILLAS INGLESAS) =7920=720*11
DIAMETRO DE LA LUNA                (MILLAS INGLESAS) =2160=720* 3
RADIO TIERRA MAS RADIO LUNA (MILLAS INGLESAS) =5040=720* 7
7920/5040=11/7 (11 DE SEPTIEMBRE/SEPTIMO/7)
5040*2*22/7=3168*10 (3168=GEMATRIA DE NUESTRO SEÑOR JESUCRISTO)
5040/(7920/2=RADIO DE LA TIERRA)=5040/3960=1.618 (NUMERO DE ORO)
 
 
21/6=MANO DE DIOS DE MARADONA
 
 
 
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From: BARILOCHENSE6999 Sent: 13/04/2018 22:57
FILOSOFIA=FILADELFIA
 
DELFIA=SOFIA (SERPIENTE PITON)
 
$=SERPIENTE
 
MONEY / MOON / LUNA
 
GOD IS GOLD

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OBVIO NEXO DE LA SERPIENTE CON LA LUNA , OSEA EL SABADO LUNAR

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From: BARILOCHENSE6999 Sent: 10/12/2018 18:56
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De: BARILOCHENSE6999 Enviado: 10/12/2018 15:09


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From: BARILOCHENSE6999 Sent: 04/01/2017 12:18
http://www.rolscience.net/2016/08/existe-la-cuarta-dimension.html

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De: BARILOCHENSE6999 Enviado: 10/12/2018 15:22
En la Biblia, la Nueva Jerusalén (también llamada el tabernáculo de Dios, ciudad sagrada, ... 185,20 metros del sistema métrico decimal actual) y 144 codos la altura de sus muros (la dimensión de uncodo en la antigüedad, se determinaba ...Y midió su muro, 144 codos, medida de hombre, la cual es de ángel." ... La Nueva Jerusalém será una ciudad celestial durante toda la Eternidad, en cuanto a ...28 oct. 2014 - La nueva jerusalem tenia 144,000 cubitos ,era un cubo y en la teoria de ... y 144 codosla altura de sus muros (la dimensión de un codo en la ...

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From: BARILOCHENSE6999 Sent: 11/12/2018 18:16

REPRODUCCION DE LOS CONEJOS EN FUNCION A LA SERIE DE FIBONACCI, INCLUSO DEL RELOJ Y DE LA MISMA SANTA CENA (MISMA MANZANA)

 
 
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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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From: BARILOCHENSE6999 Sent: 13/03/2019 14:42
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From: BARILOCHENSE6999 Sent: 17/04/2019 20:17

Madrid celebra a Leonardo da Vinci y expone sus Códices y la Tavola Lucana

Madrid celebra a Leonardo da Vinci y expone sus Códices y la Tavola Lucana

Madrid celebra a Leonardo da Vinci y expone sus Códices y la Tavola Lucana

Con el objetivo de mostrar no solo al genio sino al "hombre de carne y hueso" que fue Leonardo da Vinci, la Biblioteca Nacional y el Palacio de las Alhajas conmemoran desde hoy el quinto centenario de su muerte con una exposición que ofrece dos "joyas": los Códices de Madrid y la Tavola Lucana.

 
 
 

"Leonardo da Vinci: los rostros del genio" es el título de la exposición que ha sido presentada hoy por su comisario, Christian Gálvez, presentador de televisión y experto en la figura del maestro renacentista, y la directora de la Biblioteca Nacional (BNE), Ana Santos, quienes han destacado la oportunidad de ver tanto los Códices, los dos únicos textos de Leonardo que se conservan en España, como la Tavola Lucana, identificada como el autorretrato del italiano.

Una exposición con dos sedes, el Palacio de las Alhajas y la BNE, con las que Madrid se une a los actos de conmemoración del quinto centenario de la muerte de Da Vinci, que se cumple el 2 de mayo de 2019.

Un gran cubo con los posibles rostros de Leonardo reciben al visitante en el Palacio de las Alhajas, una forma de reflejar "la mente poliédrica de Da Vinci y la transversalidad de su conocimiento", ha explicado hoy Gálvez en la presentación de esta exposición, que enseña cómo para él era tan importante la obra acabada como la inacabada.

Imágenes de los coetáneos de Da Vinci acompañan a reproducciones de sus principales obras pictóricas, entre las que destacan "La última cena" y " La Gioconda" y sus trabajos preparatorios, junto a sus estudios de anatomía que abordó tanto con un propósito artístico como científico.

Además, la exposición ofrece numerosas maquetas tanto físicas como virtuales de las avanzadas máquinas e ingenios ideadas por un hombre "que nunca dejó de volar con la imaginación", ha indicado Gálvez.

Tras un apartado dedicado a las posibles "caras" de Leonardo, la muestra expone por primera vez en España la "Tavola Lucana", descubierta en 2008 por el historiador de arte Nicola Barbatelli, quien ha asegurado hoy que es el único retrato que reúne todas las condiciones para asegurar que representa al maestro florentino.

Estudios de pigmentación, materiales, técnicas y detalles en el cuadro han determinado que se trataba de un autorretrato de Da Vinci, ha indicado Barbatelli.

Al mismo tiempo, la Biblioteca Nacional abre hoy por primera vez su vestíbulo como espacio expositivo para mostrar dos "joyas" de sus fondos, los Códices Madrid I y Madrid II de Leonardo da Vinci.

Redactados en torno a 1500 con su escritura inversa (era zurdo), los códices son los únicos que conserva España de la colección de manuscritos que llegó a Madrid a principios del XVII: El Códice I es un tratado de mecánica y estática mientras que el II es un estudio de fortificación, estática y geometría.

Aunque la exposición permanecerá abierta hasta el 19 de mayo de 2019, los códices originales solo podrán ser contemplados un mes, en el que se irán alternando, para garantizar su adecuada conservación, ha indicado la directora de la BNE, que ha explicado que luego serán sustituidos por sus facsímiles.

Acompañarán a estos dos volúmenes otras 32 obras de la colección de la BNE que contextualizan las vida y obras de Leonardo da Vinci, así como reconstrucciones de máquinas dibujadas en los códices por el maestro y de uno de los mayores proyectos que acometió, el enorme caballo diseñado para Ludovico Sforza.

https://www.eldiario.es/cultura/Madrid-Leonardo-Codices-Tavola-Lucana_0_840616533.html

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From: BARILOCHENSE6999 Sent: 21/04/2019 14:47
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LLAVE DE ORO Y DE PLATA AL IGUAL QUE LA MANZANA
 

 


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Incendio Notre Dame: Última hora de la catedral de París (15 DE ABRIL)

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Incendio Notre Dame: Última hora de la catedral de ParísIncendio Notre Dame (París), en directo (Bertrand Guay / AFP)
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Math in Architecture and the Golden Section

 
math in architecture

The Golden Section (aka Golden Mean, and Golden Ratio) phys.org

We use math in architecture on a daily basis to solve problems. We use it to achieve both functional and aesthetic advantages. By applying math to our architectural designs through the use of the Golden Section and other mathematical principles, we can achieve harmony and balance. As you will see from some of the examples below, the application of mathematical principles can result in beautiful and long-lasting architecture which has passed the test of time.

Using Math in Architecture for Function and Form

We use math in architecture every day at our office. For example, we use math to calculate the area of a building site or office space. Math helps us to determine the volume of gravel or soil that is needed to fill a hole. We rely on math when designing safe building structures and bridges by calculating loads and spans. Math also helps us to determine the best material to use for a structure, such as wood, concrete, or steel.

“Without mathematics there is no art.” – Luca Pacioli, De divina proportione, 1509

Architects also use math when making aesthetic decisions. For instance, we use numbers to achieve attractive proportion and harmony. This may seem counter-intuitive, but architects routinely apply a combination of math, science, and art to create attractive and functional structures. One example of this is when we use math to achieve harmony and proportion by applying a well-known principle called the Golden Section

Math and Proportion – The Golden Section

Math in Architecture

Perfect proportions of the human body – The Vitruvian Man – by Leonardo da Vinci.

We tend to think of beauty as purely subjective, but that is not necessarily the case. There is a relationship between math and beauty. By applying math to our architectural designs through the use of the Golden Section and other mathematical principles, we can achieve harmony and balance.

The Golden Section is one example of a mathematical principle that is believed to result in pleasing proportions. It was mentioned in the works of the Greek mathematician Euclid, the father of geometry. Since the 4th century, artists and architects have applied the Golden Section to their work.

The Golden Section is a rectangular form that, when cut in half or doubled, results in the same proportion as the original form. The proportions are 1: the square root of 2 (1.414) It is one of many mathematical principles that architects use to bring beautiful proportion to their designs.

Examples of the Golden Section are found extensively in nature, including the human body. The influential author Vitruvius asserted that the best designs are based on the perfect proportions of the human body.

Over the years many well-known artists and architects, such as Leonardo da Vinci and Michelangelo, used the Golden Section to define the dimensions and proportions in their works. For example, you can see the Golden Section demonstrated in DaVinci’s painting Mona Lisa and his drawing Vitruvian Man.

Famous Buildings Influenced by Mathematical Principles

Here are some examples of famous buildings universally recognized for their beauty. We believe their architects used math and the principals of the Golden Section in their design:

Parthenon

The classical Doric columned Parthenon was built on the Acropolis between 447 and 432 BC. It was designed by the architects Iktinos and Kallikrates. The temple had two rooms to shelter a gold and ivory statue of the goddess Athena and her treasure. Visitors to the Parthenon viewed the statue and temple from the outside. The refined exterior is recognized for its proportional harmony which has influenced generations of designers. The pediment and frieze were decorated with sculpted scenes of Athena, the Gods, and heroes.

Math in Architecture

Parthenon Golden Section

Notre Dame Cathedral in Paris

Built on the Ile de la Cite, Notre Dame was built on the site of two earlier churches. The foundation stone was laid by Pope Alexander III in 1163. The stone building demonstrates various styles of architecture, due to the fact that construction occurred for over 300 years. It is predominantly French Gothic, but also has elements of Renaissance and Naturalism. The cathedral interior is 427 feet x 157 feet in plan. The two Gothic towers on the west façade are 223 feet high. They were intended to be crowned by spires, but the spires were never built. The cathedral is especially loved for its three stained glass rose windows and daring flying buttresses. During the Revolution, the building was extensively damaged and was saved from demolition by the emperor Napoleon.

Math in Architecture.

Notre Dame Cathedral in Paris

Taj Mahal

Built in Agra between 1631 and 1648, the Taj Mahal is a white marble mausoleum designed by Ustad-Ahmad Lahori. This jewel of Indian architecture was built by Emperor Shah Jahan in memory of his favorite wife. Additional buildings and elements were completed in 1653. The square tomb is raised and is dramatically located at the end of a formal garden. On the interior, the tomb chamber is octagonal and is surrounded by hallways and four corner rooms. Building materials are brick and lime veneered with marble and sandstone.

Math in Architecture and the Golden Section

Taj Mahal designed by Ustad-Ahmad Lahori

As you can see from the above examples, the application of mathematical principles can result in some pretty amazing architecture. The architects’ work reflects eye-catching harmony and balance. Although these buildings are all quite old, their designs have pleasing proportions which have truly passed the test of time.

 

https://bleckarchitects.com/math-in-architecture/


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