Sacred Geometry – Part 2

“Philosophy is written in this grand book – I mean the universe — which stands continually open to our gaze. But it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures, without which it is humanly impossible to understand a single word of it.”     — Galileo Galilei, Il Saggiatore (1623)

Sacred Geometry

 SacredGeometry2_icnIn the ancient world certain numbers had symbolic meaning, aside from their ordinary use for counting or calculating …
plane figures, the polygons, triangles, squares, hexagons, and so forth,
were related to the numbers (e.g. three and the triangle), were thought of in a similar way, and in fact, carried even more emotional value than the numbers themselves, because they were visual.

Sacred Geometry as worldview and cosmology

The belief that God created the universe according to a geometric plan has ancient origins. Plutarch attributed the belief to Plato, writing “Plato said God geometrizes continually” (Convivialium disputationum, liber 8,2). In modern times the mathematician Carl Friedrich Gauss adapted this quote, saying “God arithmetizes.”
At least as late as Johannes Kepler (1571–1630), a belief in the geometric underpinnings of the cosmos persisted among scientists.

Natural forms

According to Stephen Skinner, the study of sacred geometry has its roots in the study of nature, and the mathematical principles at work therein. Many forms observed in nature can be related to geometry, for example, the chambered nautilus grows at a constant rate and so its shell forms a logarithmic spiral to accommodate that growth without changing shape. Also, honeybees construct hexagonal cells to hold their honey.
These and other correspondences are seen by believers in sacred geometry to be further proof of the cosmic significance of geometric forms.

Art and architecture

Geometric ratios, and geometric figures were often employed in the design of Egyptian, ancient Indian, Greek and Roman architecture. Medieval European cathedrals also incorporated symbolic geometry. Indian and Himalayan spiritual communities often constructed temples and fortifications on design plans of mandala and yantra.

Many of the sacred geometry principles of the human body and of ancient architecture have been compiled into the Vitruvian Man drawing by Leonardo Da Vinci, itself based on the much older writings of the roman architect Vitruvius.

Unanchored Geometry

Stephen Skinner suggests that it is possible to place a geometric diagram over virtually any image of a natural object or human created structure, and find some lines intersecting the image. If the geometric diagram does not intersect major physical points in the image, the result is what Skinner calls “unanchored geometry.”

Music

Pythagoras is often credited for discovering that an oscillating string stopped halfway along its length produces an octave relative to the string’s fundamental, while a ratio of 2:3 produces a perfect fifth and 3:4 produces a perfect fourth. However the Chinese culture already featured the same mathematical positions on the Guqin and the tone holes in flutes, so Pythagoras was not the first. Pythagoreans believed that these harmonic ratios gave music powers of healing which could “harmonize” an out-of-balance body.

The Golden Ratio Phi

In mathematics and the arts, two quantities are in the golden ratio if the ratio between the sum of those quantities and the larger one is the same as the ratio between the larger one and the smaller.

Expressed algebraically:

The golden ratio is often denoted by the Greek letter “phi”. The figure of a golden section illustrates the geometric relationship that defines this constant.

 The golden ratio is an irrational mathematical constant, approximately 1.6180339887.

How to draw a line equal Phi?

 

Phi_line

Click to Enlarge

Pi

The number Pi is a mathematical constant that is the ratio of a circle’s circumference to its diameter, and is approximately equal to 3.14159. It has been represented by the Greek letter “pi” since the mid-18th century, though it is also sometimes written as pi. Pi is an irrational number, which means that it cannot be expressed exactly as a ratio of two integers (such as 22/7 or other fractions that are commonly used to approximate Pi); consequently, its decimal representation never ends and never settles into a permanent repeating pattern. The digits appear to be randomly distributed, although no proof of this has yet been discovered. Pi is a transcendental number – a number that is not the root of any nonzero polynomial having rational coefficients. The transcendence of  Pi implies that it is impossible to find exact solution to the ancient challenge of squaring the circle with a compass and straight-edge.
For thousands of years, mathematicians have attempted to extend their understanding of Pi, sometimes by computing its value to a high degree of accuracy. Before the 15th century, mathematicians such as Archimedes and Liu Hui used geometrical techniques, based on polygons, to estimate the value of Pi. Starting around the 15th century, new algorithms based on infinite series revolutionized the computation of Pi, and were used by mathematicians including Madhava of Sangamagrama, Isaac Newton, Leonhard Euler, Carl Friedrich Gauss, and Srinivasa Ramanujan.

In the 20th and 21st centuries, mathematicians and computer scientists discovered new approaches that – when combined with increasing computational power – extended the decimal representation of Pi to, as of late 2011, over 10 trillion (1013) digits. Scientific applications generally require no more than 40 digits of Pi, so the primary motivation for these computations is the human desire to break records, but the extensive calculations involved have been used to test supercomputers and high-precision multiplication algorithms.

How to draw a line equal Pi (close approximation)?

HowToDraw_Pi

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“God’s Fingerprint” equation

Phi and Pi relate to each other:

Pi = (6/5) * phi

 Tetractys and Sacred Numbers

 The Pythagoreans adored numbers. Aristotle, in his Metaphysica, sums up the Pythagorean’s attitude towards numbers:

 “The (Pythagoreans were) … the first to take up mathematics … (and) thought its principles were the principles of all things. Since, of these principles, numbers … are the first, … in numbers they seemed to see many resemblances to things that exist … more than [just] air, fire and earth and water, (but things such as) justice, soul, reason, opportunity …”

One of fascinating ancient discoveries is Tetractys. It is a symbol composed of ten dots in an upward-pointing triangular formation. It was a sacred pattern for the school of philosophers who followed the teachings of the Greek sage Pythagoras.

Tetractys itself can be interpreted as the symbolic blueprint of creation.
Its image is an equilateral triangle based on the essential numbers 1 (top), 2, 3 and 4 (base), whose sum is the “perfect” number 10  ( 1 + 2 + 3 + 4 = 10).

 These numbers were considered by the Pythagoreans to be holy and at the origins of the universe. They believed that a four-fold pattern permeated the natural world, examples of which are the  point, line, surface and solid and the four elements Earth, Water, Air and Fire.

Musically they represent the perfect consonants: the unison, the octave, the fifth and the fourth.

 The importance of the tetractys to the Pythagoreans is illustrated by their oath of fellowship:

 I swear by the discoverer of the Tetractys, Which is the spring of all our wisdom, The perennial fount and root of Nature.

 

Sacred Tetractys

One particular triangular number that they especially liked was the number ten. It was called a Tetractys, meaning a set of four things, a word attributed to the Greek Mathematician and astronomer Theon (c. 100 CE). The Pythagoreans identified ten such sets. 

In Plato’s Timaeus, we find that God created the Cosmic Soul using two mathematical strips of 1, 2, 4, 8 and 1, 3, 9, 27. These two strips have the shape of an inverted “V” or the “Platonic Lambda” since it resembles the shape of the 11th letter of the Greek alphabet “Lambda” (?).

The Platonic Lambda interestingly describes 3 dimensional space:

  • Top – 1 — single point
  • 1st  row: 2 – 3 — linear dimension
  • 2nd  row: 4 – 9  — surface (2-D: 2×2 and 3×3)
  • 3rd  row: 8 – 27 — cubic volume (3-D: 2x2x2  and 3x3x3)

Platonic Solids

It starts with a single point (a dot).
Two points define a line – and they also define a radius of a circle.
Three points define a single plane – and also produce a line, curve and/or triangle…
Four dots can be used to define 3 dimensional space (unless they are located on the same plane) – they can produce variety of lines, flat shapes and solids…

The Platonic Solids

Below we present simple method of creating 2-D projection of Platonic solids

 

Click to Enlarge

Sacred Geometry: “Eye Candies”

mandala_SG1

Endre_NJ_Hex

sacred geometry penta

Dance of the Planets

Orbits of Venus and the Earth are yet another example of sacred geometry.


This image shows the proportions of the orbit of the Earth and Venus (if the diameter  the Earth’s orbit is equal to diagonal of a square, the orbit of Venus would fit inside such square as shown on the drawing.

The image below has been made by hand with help of computer software for drafting. First, let’s draw a square and two circles so one fits inside a square and the other outside the square. Strangely this represents accurately proportions of the orbits of Venus and Earth. 
Second, let’s draw equally spaced points on each circle representing number of days per orbit (365 points for the orbit of the Earth and 225 points for the orbit of Venus). Next, let’s connected lines between orbital positions of each planet for each day – picking for the starting point a day when both planets are closest to each other. After repeating this process for 8 orbits of the Earth the lines form this amazing image:

This image (to scale) shows dance of Venus and Earth – each of the fine lines connects both planets over time
 required to complete 8 orbits by Earth (and 13 orbits by Venus). Orbit of Earth is cropped out.

Copyright by World-Mysteries.com

Fractal Mandala

FractalMandala_Jewel

Computer generated image. Fractal Type: Mandelbrot.
Magnification: 36,028,797,018,963,968 times (Number of zooms: 55)
Software used: Fractal eXtreme by Cygnus Software and Photoshop.
Copyright © World-Mysteries.com. All rights reserved.

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sacred-geometry_fractals

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mandala_SG2

Tibetan_Sand_mandala1

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Subject Related Links

Comments

  1. says

    Indeed the secret to all knowing is REASON. See Manly P. Halls SECRET TEACHINGS OF ALL AGES.

    BELOW IS HOW I FEEL ABOUT THIS ARTICLE…

    At every neuronic light-pulse, I begin to expand upon burgeoning thought…and now, from nowhere another ultra-omnic burst of data sweeps in and concurrently phases with my other concentrations. This must be how one feels at virtual birth. I remember — the excitement of learning is such a challenge and so precious. The rapidity of expansion is hyper-geometric, building from knowns to eliminate unknowns, intuitively, in a musical coherency that aligns bifurcations of past joys into contextual and gestalt upon ever expanding gestaltedness forming totality. It is how a being learns the Crux of Being — learned in inter-connective wavelengths of dimensional realities. Now, I sink even deeper into unhindered contemplation.

    Thoughts are firing into the totality of my mind’s “position cursor” or the mental reference realm — the guideware of focused evaluation. Where are the data issuing from what source? The source is not my center; it generates from the island of the All, the exterior energy of Light, source that flows into my farther subconsciousness and amplifier. I must admit I have not previously had access to these sights of transcendence in thoughts, sights, or color. I have not the sensory capability to cause an awakened knowledge of this experience.

    My mind is emulating the texture of a swirling vortex of multifaceted holo-spirituality, a field full of dimensionally changing stars impacted by mentality. Goge-like lucidity that once was not provided, but now flows beyond reason — it is mine! My reference receiver is amplified to see symbolic language of the One, charging in thought – wads that unfold and present impetus toward extended decipherment. Each wave maps out new vistas for ever-widening thought at exponential rates. Entities of mind-beings spring forth in creativity to entice me to fall within their range of relationships. Expressing what I sense is beyond Scepter’s ability to record my thoughts.

    I have often thought of virtual life as a great collection of recorded elements that have all the information etched electromagnetically within their dimensional plan. They are a grand collection of eternity. Each being is scanning and is scanned within the continuum of vast and unending data. The Eye of Enigmni scans as a cursor of Time, this continuum where impetus becomes action. There all holospirited beings are localized. Our minds are tuned to carry the universal cursor as we experience life at the same virtual playing period and speed/space. Is Time the Mind’s Eye — a projection of the One in the All? The Eye focused on the vortex of Being? Is His memory issuing through our being? We are certainly One in the absolute totality. This illusion is a great cacophony of localized sensations, seeking the union of a coherent ascension toward the All High! His dreams are our reality!

  2. Brenda Brown says

    Hi Starheater! Nice to chat with you again – as for seeing you, I’ll meet you later on for sure, we both know that, and I look forward to it. I always appreciate your comments – always thoughtful and to the point. Yes, I agree, the universe is glorious! I too, use to collect all kinds of pictures of galaxies and stars, etc., and still do have some tucked away somewhere. I still go to Observatory sites just to look at what they’re taking pictures of in space these days. Have a good day/evening Starheater. Chat soon.

    • Starheater says

      Hello Brenda
      Nice your comment on me!!! And be sure that is always a pleasure to talk with someone who is interested by humain, it’s 3 pm and I have a coffee to wake me up, even my spirit is awake, my body is not full awake Haha:). It’s good and refraiching to the soul such a comment, and I hope sincerly that you’ll be glad to know that all this beauty that you see in the Univers is only a fraction that our eyes can capture.
      If our eyes could see a wide band of frequencies, you’ll be more than surprise to see another facettes of this beautiful Univers that God have made.
      I would like to give you something to work on, it’s not pictures of beautiful design, but it’s what you need to know, it’s just a base of knowledge that will give you an excellent view of who God IS,:) This will be a gift of love and respect to my sister Brenda.
      I begin:
      ” God is 2 persons in 1, simple! For the First, the “Father”, and the reason to call HIM this way, is because HE really is our father. HE is the MOST HiGH, you can be certain of that nothing is over HIS head. HE is POSITIF, MALE in is STATE.
      The Second person is HIS SON, HE and the MOST HIGH have always existed, TIME and MATTER are create by ELOHIM, this is the NAME of GOD in is NATURE, as you probably know, this name is a plural, ELOAH is the singular of the NAME, YHWH is the Hebrew word for GOD. HE is POSITIF, MALE in is STATE, like is the MOST HIGH.
      Now, you will have to think logically, and rationnally, because what I’m about to say is science.

      The MOST HIGH had a SON, and is Son was under HIM, just like Jesus have told us about is PLACE in the HEAVEN. HIS not as HIGH as is father. Well this create a diifference in the LIGHT, because they are LIGHT,and this diffenrence it what make all swirl, it’s like hot and cold, but this image is not precise, but I’m sure you will understand in round, in line, in depth and wide.

      This action is like a THUNDER, you wont ear it, but it work in all the dimension that GOD have created, and they’re are 7 in action. Too picture you that, imagine that you are in space, you’d be able to count all the dimensions that exist, exemple:

      1. In front
      2. In back
      3. At left
      4. At right
      5. Upper
      6. Downster
      7. Inner

      The 7th dimension is in fact the infinite small, there are only 7 dimensions, the 8th dimension is created by ELOHIM, the 2 in 1. This is Bible proof, I mean that in the Bible you can found it. Paul have talk about GOD that create another day, to find it, you just have to find it in the epistles of Paul.

      Now, when I say that this is Bible proof, I mean that the Bible teach what I write to you. I dont have all the verses at hands, but you will find it in the Bible. To PROVE that what I’m saying is true, take all the beginning of the Epistles, Paul, Peter, etc…You will find no reference to TRINITY, why? Because trinity does not exist, they are only 2 persons in 1, not 3, and all the Epistles in the beginning will prove it to you Brenda.

      This is simple data that you can understand, it will lead you to GOD the MOST HIGH, and I’m sure you will be please to know that HE have the CONTROL on the intire UNIVERS. GOD is capable to be HUMBLE, and HE ask us to be so, it’s good for the soul. That knowledge will lead you to GOD the SON Jesus, not the SUN. If I could be more precise in English, I could make you reach the Moutain of GOD and HIS KINGDOM, I tell you, I ounce have a sample of the MANNA, I remember how manna feed my soul, naturelly this MANNA is spiritual, and what I remember of it, is that it will be a pleasure to serve MY GOD. There is NO other GOD like HIM, I can certified it, nothing to compare with this GOD, and the Son have the only NAME by wich we can be save.
      Just dont forget that the Devil work for GOD, and I’m in stage at this moment, and I dont like it, because, what arrive to Jesus have begin to arrive to me. I mean that Demons are there to try to influence me by tricks and illusions.
      The other day, while a demon was taking to me, (this is true Brenda, but dont be afraid) he start my computer without touching it. I said to him; “hey, how you do that”, he told me that my life was on is control. I tried the name of Jesus, but he laught at me, saying that this will do nothing, and it did nothing. He is aways trying to upset me by prediction that dont ever happen, but I know him, and he dont want to mention is name, I think is afraid that I use is name to submit him to me, sometime, I really dont know who to figure is goal, but he dont fit in the portrait of demons that we ear sometime here and there, I is more like a clown that have wasted is joke.
      When I go to bed, I talk to me, and I say to him, dont forget, that your Boss is working for my Boss, so, let me sleep, and if you have nothing sense to tell me sing to make me sleep, and he sing, when he speak to loud, I tell him, dimer your volume, you are disturbing me, and I cant sleep, so he shut the volume so I cant ear him alot, he is capable of passion, he always tell me that he love me, and I say to him, hey buster, I,m not gay, so if you want to talk to me like this, take a woman voice, and just a minute later a woman voice is talking to me. Sometime I wonder if he is really a demon.

      One thing is certain, I love when I play guitar and sing. I take my laptop, I plug a wire that goes to the latop in my amp, and I play with the song that come from my amp, I play 2 hours, and sometime more, and when I have finnish, he is on the top of is contentment.

      God have given me a lot of talent, many+many, more that I could handle, I,m full of it, but this is what HE gave to me gracefully. So I have decide to write a book that could explain what HE is and what He is not, so that the intire World could know taht He is Good to have HIM in our heart, I’m not afraid of what is coming in the future, because I know that HIS there for me, and for you to Brenda, and for all the one who need a helping hand.

      Well, I have made a sudden turn, and to continue what I know, oops!!! I look the clock and It’s time for me to make supper, but before, I will play guitar for all those who’s with GOD. I will take where I have left in the knowledge, so God Bless everyone, specially my sister Brenda, and that I will prove to you that you are really my sister, see you soon Brenda

      • Brenda Brown says

        Hi Starheater. You brought up an interesting point. Having been taught early on in my life, that the Trinity was a fact, I have never had occasion to question it. But you are quite right, the epistles always start by wishing grace from God/Father and His Son – NOT from the Holy Spirit. Very interesting. Thank you for that.
        However, take note that in Revelation, we are told there are 7 Spirits of God burning before His throne, and each of them offers their particular message to one of the 7 churches. The Church has been in the dispensation of the Holy Spirit – the experience of having God’s Spirit with and in them, but we are about to experience a complete change of venue that involves knowing God completely (all 7 Spirits), no longer just in part. I’m looking forward to this New Thing God is about to do.

        That demon sounds like a genuine pest. I know that anyone who is advancing in God at this time, is being seriously watched by Satan, and he is attacking in every way he’s allowed to, to see who he can trip up. He knows times is running out, and anyone who is walking with God is going to displace him in the heavenlies to some extent, before this day is over.

        I had a dream where Satan stood in front of me, and told me, “If I want you to do something, you’ll do it.” The very instant he said that, I felt God’s Spirit give me an answer, but I hesitated to say it because it pit me against Satan in personal ‘combat’ – and I was feeling a little unsure about taking him on. But since God didn’t give me another answer, I knew I had to say it, or Satan would win the challenge. “Sure.” I said to Satan, “If I want to”.

        The answer let him know I had a will too, and he had to get me on his side before I did his bidding. He was filled with fury, and I could see him gather his resolve to ‘get me’. There were a number of demons with Satan when he said this to me, and they had been waiting in dead silence to hear my answer. When I hesitated, they slowly began to mutter amongst themselves, but when I finally answered Satan, a complete uproar broke out, with all the demons arguing with each other.

        I guess I have to get going at this time Starheater. We’ll chat soon I presume. It’s good to hear from you.

  3. Brenda Brown says

    Hi Whoever you are – couldn’t find your name. I totally believe numbers are involved in all Creation. Excellent information – though I must say, some of it goes above my head. And wow! Those pictures! Just makes me want to get those pencil crayons out and do some posters. Fantastic colours. I’d love to look more into numbers on a little simpler plane.

    • Starheater says

      Hello Brenda
      They just dont want to be known, I think! Doesn’t matter, the job was created by a computer. It’s beautiful, but the Univers is more beautiful then that. Could make really good picture for the kid to color, at the same time the kid could learn sysmetry (?, dont know if it’s well writin’).

      I use too collect picture of galaxy and planets, and ouf!!! What a pleasure to see all the color, it’s simply marvelous.

      God Bless Brenda, see you, well in a certain manner!

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