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Phi, The Golden Ratio, and the Fibonacci Sequence
Here is a list of what phi is:
- The 21st letter of the Greek Alphabet
- The Golden Ratio (in Mathematics, Art, and Architecture)
- Electric Potential (in Physics)
- The Work Function (in Electronics)
- A Representation of Groups of Atoms in Molecules (in Organic Chemistry)
- The Fugacity Coefficient (in Thermodynamics)
- Navigation and Latitude (in Cartography/Map Making)
- The Equivalence Ratio (in Combustion Engineering)
- Representation of a Sentence (in Symbolic Logic)
- Porosity (in Geology and Hydrology)
- Strength (in Structural Engineering)
- The Roll Angle (in Flight Dynamics)
- A Generic Act (in Philosophy)
- Magnetic and Electric Flux (in Physics)
- The Cumulative Distribution Function (in Mathematics and Statistics)
- The Number of Phases in a Power System (in Electrical Engineering)
So, as you can see, we have many uses for Phi.
THE GOLDEN RATIO
QUOTED FROM WIKIPEDIA:
"In mathematics and the arts, two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. The golden ratio is an irrational mathematical constant that is approximately 1.61803398874989 (but goes on infinitely never repeating itself). Other names frequently used for the golden ratio are the golden section (Latin: sectio aurea) and golden mean.Other terms encountered include extreme and mean ratio, [5] medial section, divine proportion, divine section (Latin: sectio divina), golden proportion, golden cut, [6] golden number, and mean of Phidias.In this article the golden ratio is denoted by the Greek lowercase letter phi (  ), while its reciprocal,  or  , is denoted by the uppercase variant Phi (  ). The figure below illustrates the geometric relationship that defines this constant. Expressed algebraically:
This equation has one positive solution in the set of algebraic irrational numbers:
 [1]
At least since the Renaissance, many artists and architects have proportioned their works to approximate the golden ratio—especially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio—believing this proportion to be aesthetically pleasing. Mathematicians have studied the golden ratio because of its unique and interesting properties. The golden ratio is also used in the analysis of financial markets, in strategies such as Fibonacci retracement.
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The 9 edge-transitive convex polyhedra:
ALL OF THE FOLLOWING CONTAIN WITHIN THEM THE GOLDEN RATIO OF PHI
AT EVERY EDGE; THEY CANNOT BE FORMED CORRECTLY WITHOUT PHI
- Tetrahedron (Fire)
- Hexahedron (Earth)
- Octahedron (Air)
- Icosahedron (Water)
- Dodecahedron (Ether/Universe/Consciousness)
- Cuboctahedron (see image below)
- Rhombic Dodecahedron (see image below)
- Icosidodecahedron (see image below)
- Rhombic Triacontahedron (see image below)
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| Cuboctahedron: an Archemedian Solid; |
It is one of nine edge-transitive convex polyhedra.
Edge-transitive means that there is only one type of edge to the object;
given two edges, whatever happens on one edge will be translated or reflected onto every other edge,
without changing the original region.
| Formed by merging the Cube (Hexahedron) and the Octahedron. |
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Rhombic Dodecahedron:
This is formed by merging two Cuboctohedrons;
It is how the bee's honeycomb is formed |
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ICOSIDODECAHEDRON:
This is the closest we can come to the
shape of the earth geometrically.
Looking back at the Earth's Electro-Magnetic Field,
and the maps I have provided, (under the title "Earth")
this is where those shapes (our conscious electro-magnetic field and ley lines) come from. |
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| Icosidodecahedron |
Please click here to see how the golden ratio represents the geometric relation between all ancient sites on the planet.
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Rhombic Triacontahedron:
This is the duality of the Icosidodecahedron |
Johannes Kepler:
"Geometry has two great treasures: one is the Theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first, we may compare to a measure of gold; the second, we may name a precious jewel" (Johannes Kepler)
Kepler's Model of the Solar System:
THE GREAT PYRAMID:
Vesica Piscis:
The Vesica Piscis from the Seed of Life & The Golden Ratio:
The Egyptians Knew This Stuff!
The Eye of Horus:
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THE FIBONACCI SPIRAL:
This is the representation of PHI
This is the Fibonacci Sequence:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144,
233, 377, 610, 987, 1597, 2584, 4181, 6765,
10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, ...
The 2 is found by adding the two numbers before it (1+1);
The 3 is found by adding the two numbers before it (1+2);
And the 5 is found by adding the numbers before it (2+3);
this can go on forever in either direction (negative numbers).
Here is Pascal's triangle, which is very closely related to the Fibonacci sequence;
you'll see this later on.
It is found in the Yin-Yang:
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Here, the spiral represents FEMALE ENERGY;
and the straight lines, turning at the corners, represent MALE ENERGY.
At every 90 degree angle, the MALE and FEMALE energy meet. |
MALE AND FEMALE ENERGY:
"First I would like to say something about the nature of the male and the female. These energies are two aspects of the One. They therefore are not really opposed or dualistic, they are one; they are two faces of one energy.
The male energy is the aspect that is outwardly focused. It is that part of God or Spirit that drives outward manifestation, that makes Spirit materialize and take form. The male energy therefore knows a strong creative force. It is natural to the male energy to be highly focused and goal-oriented. In this manner the male energy creates individuality. The male energy allows you to separate yourself from the One, from the Whole and to stand alone and be a specific individual.
The female energy is the energy of Home. It is the energy of the Primal Source, the flowing Light, pure Being. It is the energy that has not yet manifested, the inner aspect of things. The female energy is all encompassing and oceanic; it does not differentiate or individualize.
Now, imagine the energy of the female becoming aware of a certain movement inside of her, a slight restlessness, a desire for… reaching out, outside of her boundaries, moving outside of herself to attain experience. There is a longing for something new, for adventure! And then an energy comes to her that answers that longing. It is the male energy that wants to be of service and help her manifest in matter, in form. The male energy defines and shapes the female energy and by their cooperation the total sum of energies can take a completely new direction. A new reality can be created in which everything can be explored and experienced, in ever changing forms of manifestation.
The dance of the male and the female brings forth the fluctuating spectacle of created reality, of your creation. This is a spectacle of great beauty wherein the male and female energy worship each other and celebrate their cooperation and playful joining. And this is as it should be. The male and female energy belong together, they are two aspects of the One and together they celebrate the joyful manifestation that Creation is supposed to be.
It has been said that in the final realization of who you are, the only truth that matters is: I AM. And in this mystical mantra, precisely those two aspects merge. In the I is the male energy, in the AM is the female energy. The I is constricting, differentiating. It gives focus, it gives direction, it individuates: I, not the other, I. And then AM. AM is oceanic, all encompassing. It reflects the ocean of Home, the female energy, the inexhaustible source that knows no bounds, no differentiation. The flowing and joining aspect is the core of the female energy. In the I AM, the male and female come together and blissfully join their energies." [FOR A CONTINUATION OF THIS QUOTE, CLICK HERE]
It can be found everywhere; from humans, to plants, to animals, to galaxies. It is the mathematical sequence of the seed of life. It is representative of a never-ending holographic universe we just so happen to live inside of. Everything is one. Everything is eternal.
^^(This is a great site.)^^
 audreythoreau.blogspot...THE GREAT PYRAMID: Vesica389 × 387 - 68k - bmp
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Now here is a thought for you: Harmonic Math
Day in the following can be viewed as the day corresponding to for instance HM 7 (ex: day 25 would be Day HM 7 )
Quote:
Opening: "In the beginning...".[Gen 1:1]
First day = HM 1: Light is commanded to appear ("Let there be light!") The light is divided from the darkness, and they are named "day" and "night".[Gen 1:3]
Second day = HM 2: God makes a firmament ("Let a firmament be...!")—the second command—to divide the waters above from the waters below. The firmament is named "skies".[Gen 1:6–7]
Third day = HM 3: God commands the waters below to be gathered together in one place, and dry land to appear (the third command)."earth" and "sea" are named. God commands the earth to bring forth grass, plants, and fruit-bearing trees (the fourth command).[Gen 1:9–10]
Fourth day = HM 4: God puts lights in the firmament (the fifth command) to separate light from darkness and to mark days, seasons and years. Two great lights are made to appear (most likely the Sun and Moon, but not named), and the stars.[Gen 1:14–15]
Fifth day = HM 5 : God commands the sea to "teem with living creatures", and birds to fly across the heavens (sixth command) He creates birds and sea creatures, and commands them to be fruitful and multiply.[Gen 1:20–21]
Sixth day = HM 6: God commands the land to bring forth living creatures (seventh command);[Gen 1:24–25] He makes wild beasts, livestock and reptiles. He then creates humanity in His "image" and "likeness" (eighth command). They are commanded to "be fruitful, and multiply, and fill the earth, and subdue it." The totality of creation is described by God as "very good."[Gen 1:26–28]
Seventh day HM 7: "Thus the heavens and the earth were finished, and all the host of them." God, having completed the heavens and the earth, rests from His work, and blesses and sanctifies the seventh day |
   we have been given the Blue Color (ie the Bible/Torah / Koran / Spiritual Gold ) ...it is up to Science to find the Red Color (the numbers once reduced would give you the corresponding numbers )  works both ways Reduction / Expansion two poles  take the example of the Healing Solfeggios...and reduce them   |
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- Another site stated to have a Black Stone was at Petra
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Salvador Dali y la geometria rombica del tigre  El cuadro completo, la granada- rombo dodecaedro, el pez -vesica piscis - sale el tigre y le rifle simbolo del fuego, caracoles con espiral aureo, la luna codigo singular 1, la mujer simboliza el 9 la Diosa levitando, detras el A-lephante con el pilar a cuestas. http://www.forocoches.com/foro/showthread.php?t=2694602&page=4 |
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015 volvamos a intentar, además explicando se aprende por que tenemos que desdoblar el conocimiento lo miramos de diferentes perspectivas lo cual nos dará una nueva visión.Aqui tienes las coordenadas del rombo dodecahedro del hipercubo, y no estan dibujadas por mi, recordemos estos números son las coordenadas cartesianas del hipercubo basadas en 4 ejes, x, y, z, y w. Por lo tanto cada punto en el espacio consta de 4 números, 4 dimensiones, punto, linea, profundidad mas el movimiento que genera nuestro tiempo.Estas coordenadas son números binarios compuestos por unos y ceros, los numeros universales, con los cuales nos envian mensajes las entidades extraterrestres, parten de cualquier dualidad, negro, blanco, prendido apagado que es el codigo morse, los números decimales son un convencionalismo.Con cualquier calculadora en la web de numeros binarios pueden constatar que el 9 y el 6 se juntan en el medio, 1001 y 0110, si los sumamos en binario como cualquier suma obtendremos 1111 que corresponde a 15.Conversor binario/decimal/hexadecimal Extraido de este link explica de Wikipedia sobre el hypercubo, Tesseract tambien en Ingles.Tesseract - Wikipedia, the free encyclopediaMe dices si vamos bien hasta aqui o me preguntasMe olvidaba de mencionar que el 9 y el 6 estan intercambiados con respecto a mi diagrama, por que los cubos se pueden intercambiar dentro del sistema, despues del fuego pasaremos a rotar en sentido inverso y este será el nuevo orden del proximo apocalipsis.El codigo moon on moday de Duran Duran, even tides, es simetrico, el codigo S-EVEN en ingles 7, quiere decir emparejar, la S es el espiral en intercambio, lo podemos ver claramente en las bombillas de luz.Tambien se puede representar con el 8 caido del Bigote de Dali, el supuesto simbolo de infinito.El museo del holcausto judio en Washingtonhttp://www.forocoches.com/foro/showthread.php?t=2694602 |
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A esto es lo que se refiere la pelicula con los numeros binariosLa mejor forma de visualizarlo y entender la realidad es mediante la proyeccion de 4 a 2 dimensiones , un grafico ejemplo de la proyeccion natural a 2 dimensiones es la sombra, recordemos que el hipercubo es una figura en constante movimiento por lo tanto tiene 4 dimensiones, en la medida que congelamos estos movimientos vamos a obtener diferentes proyecciones 2 D o sombras.   Click para ampliar Como se pueden observar esta es la proyección octogonal del hypercubo, aqui el tiempo fluye sin problemas ya que el 9 y el 6 se encuentran distantes, con el correr del mismo a traves del eje en espiral se van a ir aproximando, las proyecciones del hipercubo pasan por muy diversas formas geometricas hasta finalizar su recorrido en el rombo dodecahedro, el Codigo Da Vinci de la granada, y el panal de los Masones, ya que estos estan construidos con redes de rombos dodecahedros.Digamos que esta sería la era dorada, el codigo de las manzanas doradas y el escarabajo dorado de Jung, la forma que tomaría despues de la explosion en el centro de la galaxia que invierte los cubos y provee la energia cinetica para un nuevo ciclo.Recordemos tambien que la forma de templo de Solomon era octogonal, lo mismo muchas iglesias templarias que seguian este codigo, y la estrella de 8 puntas que hemos revisado ya en las tablas sumerias, pasando por todos los codigos Masonicos hasta el osito gominola que baila sobre la misma representando a la constelación de la osa menor.Entonces aqui tenemos las coordenadas cartesianas y binarias del rombo dodecahedro del hipercubo que es la forma que nos preocupa, sacado de Wikipedia, como veran no son mis coordenadas si no las de la propia figura, pueden comprobar que el 1001 y el 0110 son el 9 y el 6 juntandose en el medio y demas numeros referidos, caso 9-11 por ejemplo.Las calculadoras binarias estan disponibles a sola busqueda.Tesseract - Wikipedia, the free encyclopediaNotar que los angulos del medio estan levemente corridos para ubicar las dos coordenadas en el centro. Video de profesor de Matematica dibujando el hipercubo octogonal con sus respectivas coordenadas cartesianas binarias, 4 ejes, x, y, z, y w como movimiento generando el tiempo, por lo tanto cada punto esta compuesto por 4 coordenadas, y tenemo 16 puntos en el sistema, cada cubo refleja 8 puntos, recordemos nuestro cubo de dominio 6 gira en sentido antihorario, y el de dominio 9 que viene hacia nosotros como Venus gira en sentido horario, el codigo del boton.Gabi creo que esto tambien responde tu pregunta, ademas de la granada recordemos los codigos de su construcción en base al rombo, el hexagono, el triangulo equilatero, en fin todos codigos que vamos a encontrar revisando todo tipo de simbolismo, hasta en la sopa y en el chocolate toblerone - con miel de abejas !Finalmente si pudimos entender el concepto del hipercubo como la forma natural de la galaxia en constante movimiento. Entenderemos que con solo superponer el mapa estelar tendremos las coordenadas naturales de las estrellas incluido nuestro sistema solar.Facilmente podremos notar que 9-11 son las coordenadas del centro de la galaxia a nuestro sistema solar. Además de los codigos esotericos referentes al solsticio de verano como año Mason, codificado en el sol de junio dentro del Gran arco de la Fraternidad que es claramente un hipercubo, los bonfires de San Juan el Bautista que es el Oannes Sumerio representando la Vesica Piscis la cual circunda el rombo, etc, es sabido que nuestro sistema solar se encuentra debajo de Orion, por lo tanto no caben dudas de que nuestras coordenadas sean 11 y las del centro de la Galaxia 9. http://www.forocoches.com/foro/showthread.php?t=2694602&page=3 |
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Observation: copper was considered among alchemist an earthen element, if you look up platonic solids in wikipedia guess which shape corresponds to earth: hexahedron.    by just looking at the Vertices/Edges/Faces , you can tell which is the Mirror image of which or as they call them dual (or "polar") polyhedron, Tetrahedron is self dual
__________________ “Signs and symbols rule the world, not words nor laws.” - Confucius. 
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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)
HEXAGONO=OCTAHEDRO =ESTRELLA DE 6 PUNTAS= SATURNO =CUBO/HEXAGONO= ESPACIO/TIEMPO =1 DE REYES 6:20 Y APOCALIPSIS 21:16
EL SEXTO DIA ES EL VIERNES Y EL OCTAVO EL DOMINGO. INCREIBLE
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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LLAVE DE ORO Y DE PLATA AL IGUAL QUE LA MANZANA
Incendio Notre Dame: Última hora de la catedral de París (15 DE ABRIL)
 Incendio Notre Dame (París), en directo (Bertrand Guay / AFP)
PHI A NOTRE-DAME
A la catredal de Notre Dame hi observem més rectanlges auris: Creat per Mario Pastor 
The DaVinci Code, Notre Dame Cathedral from DaVinci Code
original movie prop
HEXAGONO=OCTAHEDRO =ESTRELLA DE 6 PUNTAS= SATURNO =CUBO/HEXAGONO= ESPACIO/TIEMPO =1 DE REYES 6:20 Y APOCALIPSIS 21:16
EL SEXTO DIA ES EL VIERNES Y EL OCTAVO EL DOMINGO. INCREIBLE
   
August 23, 2018/
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
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.
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.
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.
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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