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MATEMATICAS: DRAWING THE HIPERCUBE (YOU TUBE)
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Reply  Message 1 of 22 on the subject 
From: BARILOCHENSE6999  (Original message) Sent: 17/03/2013 03:07
rawing the Hypercube # 1 - YouTube
www.youtube.com/watch?v=ccws454YiVM
14/08/2008 - Subido por ProfessorElvisZap
Professor Zap shows how to draw a hyper cube in real time.
 
  • Hypercube Animation - YouTube

    www.youtube.com/watch?v=NE9ZFDJ4Phk
    06/12/2009 - Subido por brethilaki
    Video Responses · Thumbnail How to Draw a Hypercube (Tesseract) with 8 Squares by BRyanS72 2,662 ...
     
  • Discover The 4D. The Impossible Hypercube. - Video

    www.metacafe.com/.../discover_the_4d_the_impossibl...
    03/06/2007
    I am drawing there the HYPERCUBE; a cube that is impossible to imagine in a 3D world. Th. Watch Video ...

  • Anuncios:

    First  Previous  8 to 22 of 22  Next   Last  
    Reply  Message 8 of 22 on the subject 
    From: BARILOCHENSE6999 Sent: 17/03/2013 03:46

    Hypercube construction

    27 February 2008 at 11:22 am (Mechatronics, Un-Usual Post, Videos)

    I’ve decided to write this post in order to try to give an answer to Eggshell Robotic question “Tesseract / Hypercube – Mechanical Possible?“… The main reason to make a post on my blog rather then making a comment on Eggshell Robotic’s post is mainly the fact that I wrote a lot… and I use images and links… so here it is :

    A hypercube is basically 8 cubes organized using the same logic as we use to build a square (2 dimensions) with strokes (1 dimension), and to build a cube (3 dimensions) with squares (2 dimensions)… We take the first cube, join its 6 faces with one face of 6 other cubes… then we go to the 4th dimension by joining all faces that are next to each other… The 8th cube is used to close the hypervolume…

    It might be easier to explain it comparing to the cube construction… We have 6 squares (2D) we take one to use as center. We join 4 other squares around the one in the center… (still in 2D)… Now we rotate the 4 new squares to the upper dimension in order to link theme (now we are in 3D) but the cube is not closed, therefore we have a 6th square to close the missing face of the cube… Here is a site showing part of the process.

    http://beart.wordpress.com/2008/02/27/hypercube-construction/


    Reply  Message 9 of 22 on the subject 
    From: BARILOCHENSE6999 Sent: 17/03/2013 03:49

    Hypercubes

    The most famous example of a higher dimensional object is the hypercube. Broadly speaking, the hypercube is to the cube as the cube is to the square. But, what does this mean? What can we determine about the geometrical properties of the hypercube?

    The best way to grasp a picture of the hypercube is to work up to it dimension by dimension. We can start in zero dimensions and proceed onwards to produce a whole family of cubes. A point does not have any extension. It is the unique zero dimensional object. If we allow our point to sweep out a length of one unit, say along the x axis, we can produce a line segment. Next we can allow the line segment to sweep out a distance of one unit in a perpendicular direction, say one unit along the y axis. The figure that we will produce is a square. Next, our square can sweep out a distance of one unit in a direction perpendicular to the first two directions, say the direction along the z axis. The result will be a unit cube.

    What happens next? We now seem to have run out of perpendicular directions in which we can continue this procedure. However, we can imagine that there are further perpendicular directions and envisage abstract higher dimensional space. There is no reason why we should restrict ourselves to the three dimensions of physical space; as long as we reason clearly and consistently, we can deduce the mathematical properties of higher dimensional objects, even if they cannot be physically realised in our three dimensional universe. We can simply declare that we are now working in four dimensional space and see where our exploration leads us. If we find ourselves in an interesting place, then that will be sufficient reward for our journey. Often the research of pure mathematicians is guided by the search for interesting abstract scenery rather than a quest for scientific utility. In our abstract four-dimensional space, there will be a fourth axis that is perpendicular to our other three axes. We can label this axis the w axis. Measuring the distance parallel to each of the four axes gives us four coordinates that will specify the position of any point within our four dimensional space.

    With a fourth perpendicular direction that we might label the w axis, we can now take the cube and sweep it one unit along this direction. The object that we will generate is the four dimensional equivalent of the cube. It is the object of our dreams, our hypercube. So what does it look like? Is there any way that we can visualize it?

    Our sections through a cube formed a sequence of squares. And similarly, our sections through the hypercube form a sequence of cubes. [We can imagine going down to two and one dimension to see how the analogy works in the case of the two-dimensional cube, which we usually call a square and the one-dimensional cube, which we usually call a line segment. (Our sequence of sections of a square are a sequence of line segments. Our sequence of sections of a line segment is a sequence of points.)]

    What else can we infer from this description of a hypercube? If we draw the hypercube with an exaggerated perspective it will help us to understand the analogy with a cube. First we can draw a transparent cube face-on, so that we can see the back face within the front face and with edges connecting the corners of the front face to the corners of the back face. We can make a similar drawing of a transparent hypercube. If we position the hypercube in the same orientation as in our previous discussion, in our perspective drawing we will see a large cube, with a smaller cube within. Each of the corners of the outer cube are connected by edges to the corners of the inner cube. What we are looking at is the front cube (the outer cube) with the back cube, which is further away in four-dimensional space, appearing within it because its size appears diminished with distance. This is completely analogous to seeing the back face of the transparent cube within its front face.

     
     
       
     
     

    In the projection shown above, the front and back squares of the cube both look square, but the other four square faces of the cube do not look square. Similarly, in the projection of the hypercube, the front and back cubes of the hypercube both look cubical, but the projection has distorted the shapes of the other six cubes that form the hypercube. However, there are more symmetrical ways to project a hypercube down to two dimensions, in which the distortion is shared equally between all eight cubes. Such a projection is shown below. It gives a better feel for the structure of the hypercube. The outlines of each of the eight cubes can be picked out in this projection.

     
     
       
       
     
     
     

    In the illustration shown above right, the axes have been given arbitrary labels: 'w', 'x', 'y' and 'z'. In four-dimensional space these would be the four mutually perpendicular axes. In this projection down to two dimensions, the 'w' and 'y' axes remain perpendicular and the 'x' and 'z' axes remain perpendicular, but the angle between the 'w' axis and the 'x' axis is now 45°.

     
     
         
     
     

    On the left above, the twelve edges of one of the 8 cubic cells of the hypercube have been coloured red. The edges and faces of this cube are aligned with the 'w', 'x' and 'z' axes. In four-dimensional space, this cube is perpendicular to the 'y' axis. On the right, the edges of the opposite cubic cell have been coloured magenta. If we were looking along the 'y' axis, these would correspond to the front and back cube of the hypercube. Note that each corner of one cube is connected to a corner of the opposite cube by a blue edge that is oriented in the 'y' direction, the direction that is perpendicular to the two cubes.

     
     
     

    The image below shows a three-dimensional projection of the edges of a hypercube. The shadow of the hypercube is the two-dimensional projection that we have been considering above. In a sense the three-dimensional figure is a three-dimensional shadow of the four-dimensional hypercube.

     
     
     

    Reply  Message 10 of 22 on the subject 
    From: BARILOCHENSE6999 Sent: 17/03/2013 03:53
  •  

    How to Draw a 4D Hypercube (My Way)

     
    thatsketchygirl.hubpages.com/.../How-to-Draw-a...En caché - Traducir esta página
    21/12/2011 – If you're drawing a square on a flat sheet of paper, how many straight lines does it take? Four. If you're drawing a cube, how many squares ...
  •  
    [PDF] 
     

    Drawing the Hypercube - University of South Alabama

    www.southalabama.edu/.../DrawingtheHypercub...  - Traducir esta página
    Formato de archivo: PDF/Adobe Acrobat - Ver en versión HTML
    Acknowledgement. This talk was supported by the Ministry of. Education Science and Technology (MEST) and the Korean Federation of Science and ...
  •  

    How to Draw a hypercube « Math

     
    math.wonderhowto.com/how-to/draw-hypercube...En caché - Traducir esta página
    24/03/2010 – This clip shows how you can draw a hypercube, which is a complex shape composed of cubes. You start with a series of equally spaced ...
  •  

    Like Scratches in the Sand - Tesseract Tutorial

     
    odditycollector.livejournal.com/173945.htmlEn caché - Similares - Traducir esta página
    How to draw a 4-D hypercube without having to actually understand the math! In case, I don't know, this is a skill you think you will need someday.
  •  

    Skeptic's Play: Hypercubes and hypercube nets

     
    skepticsplay.blogspot.com/.../hypercubes-and-hy...En caché - Similares - Traducir esta página
    04/03/2008 – The hypercube is hard to draw! I often try to draw hypercubes in the margins of my notebooks when I should be listening to lectures (true story!).
  •  

    Hypercube

     
    www.mathematische-basteleien.de/hypercube.htmEn caché - Similares - Traducir esta página
    What is the Hypercube? Cubes in Perspective Central Projections Nets Cross- Sections, More Drawings The n-dimensional Cube The Hypercube on the Internet ...
  •  

    Hypercube - The Geometer's Sketchpad Resource Center

     
    www.dynamicgeometry.com/.../Hypercube.htmlEn caché - Similares - Traducir esta página
    ... to my friends how a multidimensional object can be visualized in two-space, or what it means to "draw a picture" of a hypercube (a four-dimensional object).
  •  

    Reply  Message 11 of 22 on the subject 
    From: BARILOCHENSE6999 Sent: 17/03/2013 04:02

    64 – DNA – Mayan’s AINTIRAM – NaSSim Haramein – Tesseract – Hypercube

    WE ARE THE 99%

    DNA says so …

          

    The above book DNA AND THE I CHING was published in the 1990s, the youtube interview featuring Nassim Haramein below is recent.
    On the cover of the book we see a cube, specifically a 4x4x4 cube comprised of 64 smaller cubes.
    If we rotated the cube so we could see only one face, it would appear as a 4×4 square, comprised of 16 squares.

    64

    Obviously the word ‘amazing’ that Nassim Haramein uses in reference to his epiphany regarding the ancient text Aintiram, does NOT have a best before date that can expire.
    Obviously everybody proceeds at their own speed and pace, and what was amazing yesterday to one person, will still be amazing in the future to another person just waking up.

    The importance of the number 64

     Arrow   FRACTALS – KEYHOLE – DNA – ANKH – LAPIS EXILLIS

    Tesseract – Hypercube – Maltese Cross – Crucifix – cube within the cube – wheels within wheels …

    Arrow   ‘IN THIS SIGN CONQUER’ the Great Pyramid and the Sacred Cut by Tons Brunés leads us to Nikola Tesla and the Philosopher’s Stone

    Dalí — Crucifixion (Corpus Hypercubus)According to the Oxford English Dictionary, the word “tesseract” was coined and first used in 1888 by Charles Howard Hinton in his book A New Era of Thought, from the Greek τέσσερεις ακτίνες (“four rays”), referring to the four lines from each vertex to other vertices. Some people have called the same figure a tetracube, and also simply a hypercube (although the term hypercube is also used with dimensions greater than 4).

    This is a great great article:

    Unfolding the Tesseract an 8-cell

    by Peter Turney

    http://unfolding.apperceptual.com/

    AHA!

     

    I see YHVH trapezoid geometry in the 5 sections of the Cut Cube image on the right.
    I see the numbers 5 6 7 8 written on the apex indicative of the corners.
    I see a Maltese Cross and a blueprint we can place over the Great Pyramid.
    (see image/links below)

    5 6 7 8 = 26

    But here is the wow.
    After my neighbor of many years died, his daughter held a contents sale.
    I picked up a few items that belonged to John P., one of them was an odd plaque that simply had the numbers 5 6 7 8 placed on it.
    It is clear from the items that found their way to me, that ole’ John P. had probably attended some Freemason meetings in his life.
    After all he was a cop for 31  years so that does not surprise me.

    Nassim Haramein – Sacred Geometry & Unified Fields

    Drawing the Hypercube # 1

    Tesseract Pencil Visualization

    Imagining the Tenth Dimension part 1 of 2

    Swastika + pi + phi + Speed of Light = Great Pyramid

    It might help before proceeding to have a quick look at this link first:
    http://kachina2012.wordpress.com/2011/12/15/the-sacred-cut-by-tons-brunes/

    DNA is the common denominator that links the we are the 99% .
    Even the 1% belongs to the 99% as defined by DNA.

    note the Friendship Knot that is made by 4 hands in an embrace.

    … follow the forearm to the 4 bends in the 4 elbows >>> so what symbol that helps define CW or CCW movement comes to mind?

    Does CHASE Bank want to be counted among your friends?

    If you do not enjoy this documentary I will refund you your funny Freedom 55 CHASE the money.

    REVELATIONS of the PYRAMIDS

    Arrow   http://www.youtube.com/watch?v=SmnnJytYjpM

    Many AHA to be found among the ruins in that documentary.
    Did you know that the first king of Egypt called Menes by the Greeks was know as King AHA!


    Relationship of both the great pyramid and the swastika to the squared circle, aka pi using two circles?

    i.e.
    Go to 1:18:20 of that video.
    listen carefully to what is being said about the two circles being drawn relative to a square pyramid with eight sides.

    Is the speed of light mentioned along with pi?

    These next mages were taken out of books printed in and around 1923.

    Note in the first image, we have those 4 special constellations mentioned in the documentary, highlighted in the four corners.
    i.e. The Man, the Eagle, the Lion, the Bull

    …similar geometry. Is it difficult to connect the star of david to the square or cube?
    Not at all.

    And throughout the video we saw how they divided the Great Pyramid into eight sections, not four.

    Go to 16:00 of that video for a discussion of the 8 sided pyramid.

    Does the 8 sided pyramid whose 8 sides can only be seen briefly during the two equinoxes have any relationship to the BaB-iLu and the BiBLe?

    BaB-iLu is similar to BiBle with the vowels removed…BBL….so is BaBeL, BiBLioS, BaRBeLoS, and the word QiBBLe which is the root of the word CaBaLa.

    GeNeSiS is GNoSiS, or both can be written GNSS, if you remove the vowels.

    I did promise you an aha or two.

    Now you need to find the match to those hexagons/trapezoid in the next image.


    Temple of Man Schwaller de Lubicz page 177 Serpents in the Sky by John Anthony West

     

    WTF 911

    WTC 7 is the same shape as the YHVH trapezoid? 

    YHWH = 26
    QaBaLaH =137

    Arthur I. Miller ends his book ‘137‘ discussing the ‘26‘ constants physics is currently using trying to formalize a ‘theory of everything’.

    Yes 26 of course….and 137 is the most fundamental of them ALL encapsulating 3 other constants into ONE dimensionless constant.

    Now would be a good time to introduce the work of engineer Tons Brunes and his insights into geometry.

    Specifically ‘the Sacred Cut’.
    Arrow   http://breakfornews.com/forum/viewtopic.php?p=74451#74451


    Reply  Message 12 of 22 on the subject 
    From: BARILOCHENSE6999 Sent: 17/03/2013 04:03

    Reply  Message 13 of 22 on the subject 
    From: BARILOCHENSE6999 Sent: 18/03/2013 04:21
     

    Hypercube Animation - YouTube

    www.youtube.com/watch?v=NE9ZFDJ4Phk
    06/12/2009 - Subido por brethilaki
    Video Responses · Thumbnail How to Draw a Hypercube (Tesseract) with 8 Squares by BRyanS72 2,662 ...
     
    EL DIBUJAR EL HIPERCUBO, EN EL CONTEXTO AL OCTOGONO, NOTEMOS EL PEQUEÑO CUADRADO COMUN A LOS DOS CUBOS, QUE SE DIBUJAN ES EN UNA RELACION DE 2/8=1/4. CONCRETAMENTE LA PARTE EXCLUIDA, OSEA NO COMUN, ES 6/8=3/4 O VICEVERSA 8/6=4/3=1.33. AQUI ESTARIA EL SECRETO DEL NUMERO 33, EN FUNCION AL OCTOGONO.

    Reply  Message 14 of 22 on the subject 
    From: BARILOCHENSE6999 Sent: 13/04/2013 02:27



    Reply  Message 15 of 22 on the subject 
    From: BARILOCHENSE6999 Sent: 29/08/2013 07:08

    Reply  Message 16 of 22 on the subject 
    From: BARILOCHENSE6999 Sent: 29/08/2013 07:09

    Reply  Message 17 of 22 on the subject 
    From: BARILOCHENSE6999 Sent: 25/10/2014 22:38
     
    Fermentation - nigredo - bread and wine of Christ

    Image


    Image


    Image

    La vesica piscis (vejiga de pez en latín) es un símbolo hecho con dos círculos del mismo radio que se intersecan de manera que el centro de cada círculo está en la circunferencia del otro. Esta forma se denomina también mandorla (que significa "almendra" en italiano).
     



     
    Se  produce el mismo patron. LA SERPIENTE SE MUERDE LA COLA.



    EL RELOJ DE ARENA TAMBIEN TIENE UN AGUJERO DE GUSANO Y CUMPLE EL MISMO PATRON.EL ORIGEN DEL PORQUE EXISTEN DOS PERIODOS DE 12 HORAS EN EL DIA, TAMBIEN TIENE ESTE NEXO E INCLUSO TAMBIEN CON EL ZEP TEPI DE LA PRECESION DE LOS EQUINOCCIOS.
     
    4 FASES DE LA LUNA (MES LUNAR)
    4 EXTREMOS DIARIOS (AMANECER-MEDIO DIA- PUESTA DEL SOL Y MEDIA NOCHE)
    4 EXTREMOS ANUALES (DOS SOLSTICIOS Y DOS EQUINOCCIOS)
    4 EXTREMOS PRECESIONALES (ACUARIO- LEO - ZEP TEPI - TAURO Y ESCORPION)
    ES OBVIO EL FRACTAL
    AMANECER-PUESTA DE SOL= ZEP TEPI =DOS EQUINOCCIOS (22/3 Y 22/9) =LUNA LLENA Y LUNA OSCURA (1ERO Y 15VO DIA LUNAR DEL MES)
    CRUZ=4 EXTREMOS
    True Cross.jpg 
    ‘True Cross’ Cathedral Lisieux, France

    True Cross2.jpg
    ‘True Cross’, Baselique Notre Dame d’Ouvres La Delivrande, France

    In churches, the four signs of the Zodiac often reoccur and are associated with ‘Judgment Day’ and the ‘End of Times’

    Judgement Day.JPG
    Jesus portrayed at the Last Judgment can often be found in the Tympanium above the entrance of churches and cathedrals. Notice, the lion (Leo) on the left, the bull on the right (Taurus), the angel on the left (Aquarius) and the eagle on the right ( Scorpio).

    The four evangelists Luke, John, Mathew and Mark likewise have been associated with these four Zodiac signs as well:

    JohnLukeMarkMatthew
    Mark = Scropio (Eagle),          Luke = Taurus,                  John = Leo,              Matthew = Aquarius


    Reply  Message 18 of 22 on the subject 
    From: BARILOCHENSE6999 Sent: 26/10/2014 02:07
     
    En geometría un teseracto o hipercubo es una figura formada por dos cubos tridimensionales desplazados en un cuarto eje dimensional (llamemos al primero longitud, el segundo altura y el tercero profundidad). En un espacio tetradimensional, el teseracto es un cubo de cuatro dimensiones espaciales. Se compone de 8 celdas cúbicas, 24 caras cuadradas, 32 aristas y 16 vértices, esto tomando en cuenta el desarrollo del polinomio (2x + 1)n donde el valor de n equivale al número de dimensiones (en este caso particular 4) y x es el largo, alto, ancho, etc., de la figura polidimensional equilátera.

    Este término fue acuñado por primera vez en 1888 por el matemático inglés Charles Howard Hinton en una obra llamada A New Era of Thought, especie de manual que buscaba entrenar la intuición hiperespacial mediante ejercicios de visualización con cubos de colores en torno a un hipercubo imaginario.

    Un hipercubo se define como un cubo desfasado en el tiempo, es decir, cada instante de tiempo por el cual se movió pero todos ellos juntos. Por supuesto no podemos ver un hipercubo en la cuarta dimensión, ya que solo se verían los puntos que tocan nuestro universo, así que solo veríamos un cubo común.

    No podemos ver un hipercubo porque estamos sujetos a tres dimensiones, por lo que solo podemos ver la proyección de lo que seria un hipercubo. Se parece a dos cubos anidados, con todos los vértices conectados por líneas. Pero en el teseracto real de cuatro dimensiones todas las líneas tendrían la misma longitud y todos los ángulos serían ángulos rectos.


    si se fijan en el simbolo de la kabbalah Judia del arbol de la vida y vemos claramente
    la estrella de david (simbolo del judaismo) y tambien vemos que es un hipercubo
    todo esto es parte del codigo biblico???

    Reply  Message 19 of 22 on the subject 
    From: BARILOCHENSE6999 Sent: 09/02/2016 23:52
     
    Hypercube or Tesseract 32 sides encoding 32 paths of Masonic hierarchy before the invisible top 33 symbolizing breaking through the other side.

    http://sealrevelation.blogspot.com.ar/search/label/11111
     
    Image


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    Reply Hide message Delete message  Message 2 of 2 on the subject 
    From: BARILOCHENSE6999 Sent: 09/02/2016 20:44
    Fermentation - nigredo - bread and wine of Christ

    Image


    Image


    Image

    La vesica piscis (vejiga de pez en latín) es un símbolo hecho con dos círculos del mismo radio que se intersecan de manera que el centro de cada círculo está en la circunferencia del otro. Esta forma se denomina también mandorla (que significa "almendra" en italiano).
     



     
    Se  produce el mismo patron. LA SERPIENTE SE MUERDE LA COLA.



     
    EL MISMO CUBO ESTA DISEÑADO EN FUNCION AL NUMERO 12, EN EL CONTEXTO A LAS 12 HORAS DEL RELOJ. EFECTIVAMENTE TENEMOS 4 LINEAS EN LA PARTE SUPERIOR, 4 EN LA PARTE CENTRAL Y 4 LINEAS EN LA INFERIOR (4+4+4=12). EN EL MARCO AL HIPERCUBO, ADONDE TENEMOS 2 CUBOS COMO PODEMOS OBSERVAR EN LA PARTE SUPERIOR, TENEMOS UNA REFERENCIA OBVIA A LAS 24 HORAS DEL DIA, OSEA 12+12=24. ES OBVIO EN ESTE MARCO QUE EL PATRON DEL HIPERCUBO RESPONDE AL DIA DE 24 HORAS. TODO ESTO ES UNA OBVIA REFERENCIA A HECHOS 12:12, OSEA JUAN MARCOS. EL MISMO PATRON EN EL CONTEXTO AL NUMERO 8 DE LA PLAZA DE SAN PEDRO, TAMBIEN RESPONDE AL PATRON DE LAS 24 HORAS= 8*3 HORAS= 1440 MINUTOS= 8*180 MINUTOS= 86400 SEGUNDOS= 8*10800 SEGUNDOS
     
     
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    Reply  Message 20 of 22 on the subject 
    From: BARILOCHENSE6999 Sent: 12/07/2018 17:01
    ¿COMO EXPLICAS EL NEXO 911 CON EL DIA DE MARIA MAGDALENA EN EL MARCO A LA INDEPENDENCIA DE EEUU EN FILADELFIA?
    11/9/2001-11/9/2005=1461 DIAS
    11/9/2005-22/7/2006=315 DIAS
    1461+315=1776
    EL 4/7/1776=INDEPENDENCIA DE EEUU EN FILADELFIA
     
    Image
    En aquel tiempo, respondiendo Jesús, dijo:
    Te alabo, Padre, Señor del cielo y de la tierra,
    que hayas escondido estas cosas (la Gnosis, la Sabiduría Oculta)
    de los sabios (de los eruditos) y de los entendidos, (de los intelectuales)
    y las hayas revelado á los niños. (A los Iniciados). Así, Padre, pues que así agradó en tus ojos."
    (Mateo 11: 25-26).
     
    EL PATRON KAVALISTICO DE LA INDEPENDENCIA DE LOS ESTADOS UNIDOS ESTA TOTALMENTE INTERRELACIONADO CON LAS BODAS DE CANA, EN EL CONTEXTO A QUE LA MISMA NO FUE SOLAMENTE EN UN TERCER DIA ( JUAN 2:1), SINO QUE TAMBIEN EN UN SEPTIMO DIA (JUAN 1:29,35,42 Y JUAN 2:1). DE ALLI SALE EL MONSTRUSO NUMERO 37.
     
    1776=48*37
    666=37*18
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    37*18=666
    37*48=1776 (AÑO DE LA INDEPENDENCIA DE EEUU)
    LA MISMA TORRE ES UN SIMBOLO FALICO CON FUERTE CONNOTACION SEXUAL

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    From: BARILOCHENSE6999 Sent: 30/11/2018 17:49
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    Resultado de imagen para JUAN 3:14
    22/7=3.14=PI
     
     
    12 PUNTOS EN SU CIRCUNFERENCIA=RELOJ=SANTA CENA
     
     
    LONGITUD CIRCUNFERENCIA=PIxDIAMETRO
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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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    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

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    EL SEXTO DIA ES EL VIERNES Y EL OCTAVO EL DOMINGO. INCREIBLE
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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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