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In this article we will take a look at some various ways in which the Triad is manifested and used in physical reality.  We will focus heavily on the geometry of light, color and sound as they relate to triangles and the 3D triangle, the tetrahedron.

the sun 2027310 1280

 

 

Triangles in Architecture & Design

The triangle is the quintessential symbol of the Triad.

The triangle bestows strength, balance, and efficiency of space, energy and materials, therefore it is used often in architecture and engineering.

The triangle can balance visual appeal and symbolism in architecture.

architectural design 3481765 1920 roof 2436932 1920

architecture 2350468 1920 home 2668534 1920

parthenon 2287872 1920

Parthenon replica, Nashville, TN

 

In engineering triangulation creates stability.

roof truss 3339206 1920

 

Triangles employ the principle of stability in the A-frame truss.

Aframe church A Frame

 

Forces push inwards from the bottom points, downwards from the apex, and outwards from the bottom points – creating a perfect balance.

Carpenters stabilize a structure by bracing it with triangles and Ladders are triangular as they are the most stable shape.

architecture 441315 1920

 

Arches use the principle of the triangle’s stability to remain standing.

2000px Arch brace truss 3D.svg Lusthaus Truss

Forces push upwards into the arch, downwards from the apex and outwards from the apex through the legs.

This triple-structure architecture stands due to the triple forces balancing the structure.

bridge 918575 1920

 

 

As Leonardo da Vinci said, “An arch is two weaknesses which together make a strength.”

river 2681380 1920

 

Triangles are also seen in dams, tunnels, bridges, geodesic domes and monuments such as the Eiffel Tower and the many pyramidal structures found throughout the world.

black and white 50272 1920 brooklyn bridge 105079 1920

architecture 1851116 1920 tunnel 2325753 1920

eiffel tower 3349075 1920 golden gate bridge 388917 1920

louvre 102840 1280 egypt lowres

 

Triangles give the wedge and ax their splitting power.

tents 2526902 1920

 

The arched triangular indentation in the base of a wine bottle simultaneously strengthens the container and collects sediment.

wine cellar 3121221 1920

 

 

 

The Triad Geometry of Knots & Braids

Knots and braids take three parts interlocking simultaneously to become unified.

No knot can have fewer than three crossings.

A trefoil knot is the simplest possible continuous-line knot.

rope 1469244 1920

 

Braided hair requires three tresses. Two tresses twirled around one another will not hold. The third tress locks in the braid.

person 3345654 1920

 

“That is, the Dyad’s principles will not create an enduring whole but merely opposites without resolution, and unending dance of conflict, like lawyers without a judge.”1

A third strand will create a self-enforcing stable unity.

 

 

 

Triads in Natural Forms

There are three parts of an insect – head, thorax abdomen.

triad insect

 

There are three main parts of a human body – head, torso, legs.

skeleton 1243818 1920

 

Three-petaled flowers are the beginning of every fruit and vegetable. There are also three-petaled flowers and leaves not related to vegetables.

three marys 725882 1920 three master of flowers 2393312 1920 clover 883210 1920

 

Many fruits and vegetables display three-corner structure.

cuc triangle melon triangle pepper triangle

The triangle gives the rose’s thorn its efficacy. The same goes for other thorned plants.

flower 832217 1920 thorns 466335 1920

 

It also gives the shark tooth its bite.

hai 1093273 1920

 

The Triad is seen in the way coequal molecular bonds tear apart and break into three-way 120-degree joints.

120 Joint

This is seen in more elastic materials that crack relatively rapidly over hours, days, and months.

Examples are seen in concrete and rocks, drying mud, coffee grounds in the filter, and bullets piercing an egg.

cracked mud cracked stone

cracked stone wall bullet piercing egg gary s settles

Credit: Gary S. Settles

 

Longer times, like years, decades, or centuries, result in a four-cornered rectilinear pattern. This will be discussed in the Tetrad section and can be seen in things such as old paint and porelain.

jug 316136 1280

 

Furthermore, after 3 years the Moon closely repeats its phases in the calendar.

a total solar eclipse 1113799 1920

 

 

 

Delaunay Triangulation and Voronoi Tessellation

Delaunay Triangulation and Voronoi Tessellations are a process that nature undergoes to form many structures in nature. These include molecular structures and cellular structures of plant seeds, pollen, roots, leaves, flowers and fruits, as well as the cellular structure of fungi, insects and insect wings, and the cellular structure of many animal and human tissues.

It is important to understand how this process works geometrically to see why it is so commonly used by nature.

It is all based on triangles.

 

“The implication is that when a single point relates to two other points in space it becomes a generating angle or vector.”2

In the article Nature by Numbers3 it says, Voronoi Tessellations “are based on a distribution pattern that is easily recognizable in many natural structures, like the wings of some insects and plant leaves.”

The article goes on to show how Voronoi tessellations and Delaunay triangulation can form the structure of a dragonfly wing.

voronoi 4

 

Delaunay triangulation involves a set of discrete points on a plane. Triangles are formed among the points so that no outside point falls in the circumcircle of the triangles. Connecting the centers of the circumcircles produces the Voronoi tessellations that are hexagonal and pentagonal in structure.

Visit: http://www.scienceonthenet.eu/content/article/nature-numbers to see clearly what is going on here.

voronoi 1 voronoi 2 02b voronoi 3

 

Delaunay triangulations maximize the minimum angle of all the angles of the triangles in the triangulation. They tend to avoid sliver triangles (extremely acute triangles that look like slivers).

 

Reference Construction Lesson #29: Delaunay Triangulation and Voronoi Tessellations.

B1 wine 1740554 hexad nature3

bazzania tricrenata 903625 1920 bazzania fflaccida microscopic cells biology macro science plant botany 862774.jpgd

breadfruit insect wings

Pollen 15 Seed 10 Seed 21

Credit: Rob Kesseler, Seeds & Pollen

 

 

Triads in the Human Body4

The sacrum of the pelvis is a triangle. This allows for a stable, seated posture. The sacrum is also the keystone supporting our body when we stand.

 

The scapula (shoulder blade) is roughly triangular. There are three borders. This shape both stabilizes the arm and provides for a wide range of movement at the shoulder. In fact the shoulder joint is the joint with the largest range of motion in the body.

1024px Scapula posterior view2

 

Three types of bone cells:

  • osteoblasts – creates new bone and repairs old bone by extracting calcium from the blood and laying down new bone matrix (creation)
  • osteocytes – maintain and repair the bone’s substance and strength (preservation)
  • osteoclasts – dissolves and re-assimilates old bone materials by dissolving bone matrix into the blood (destruction – transformation)

 

Three body planes: frontal, sagittal, transverse

Planes of Body

 

Three layers of skin: Epidermis, Dermis, Subcutaneous layer

skin layers

 

Three germ layers: endoderm, mesoderm, ectoderm

These germ layers are groups of cells in an embryo that interact with one another to form all organs and tissues of the developing human.

germ layers in animals

 

Three life support systems of the human body: brain, heart, lungs (nervous, circulatory, respiratory).

anatomy 2328534 1920

 

Three main parts of the cardiovascular system: arteries, veins, heart.

earth fractal 6

 

Three phalanges for each finger/toe.

1063px Scheme human hand bones en.svg

 

Three semicircular canals in the vestibular apparatus.

These are responsible for balancing, as well as some unpleasant experiences like motion sickness. There is one for each axis of 3D space.

Blausen 0328 EarAnatomy ear canals

 

Three major nerves in the forearm: Radial, Ulnar, and Median.

Three sections of the small intestine: duodenum, jejunum, ileum. This is where the vast majority of nutrient uptake occurs.

2417 Small IntestineN

 

Three types of muscle: smooth, cardiac, and skeletal

muscle tissues

 

Three muscles of the anterior abdominal wall: External oblique, Internal oblique and the Transversus Abdominis.

These abdominal muscles in conjunction with the three erector spinae muscles of the back serve to keep us in a stable upright posture as we stand and walk.

trunk muscles

 

Many other muscle groups of threes:

  • triceps brachii (three-headed muscle of the arm)
  • deltoids: triangular shaped (anterior, lateral, posterior)
  • hamstrings (semimembranosus, semitendinosus, biceps femoris)
  • gluteals (maximus, medius, minimus)
  • erector spinae (Iliocostalis, Longissimus, Spinalis)

 

There are also many examples of Triads in the circulatory and nervous systems.

 

 

 

The Triad and the Geometry of Light

In Article 23 we discussed the geometry of light in regards to the Vesica Piscis and the Dyad. Here it is important to see that the Triad – the equilateral triangle – emerges directly from the Vesica Piscis. In three dimensions this equilateral triangle is a tetrahedron.

2 vesica piscis triangle lin art tetrahedron1

 

A tetrahedron is a balance of the Triad (triangle) and the Tetrad (4-faces). The triangle is a balance of the Dyad (Vesica & line) and the Triad (3-sides). All of this comes from the Monad (the pulsating rotating circle/sphere that reflections itself in infinite directions).

It is important to remember that the principles of the Dyad, Triad, Tetrad…etc. never work in isolation. They are always interwoven with the principles of all the numbers from 1 to 10.

prism

 

We learn in the Science section of Cosmic Core that the Photon is Tetrahedral in nature. See Article 124 for more information.

 

This was first predicted by Buckminster Fuller, Max Planck and physicist Rod Johnson.

The core of the photons identity is geometric, just as the nature of all vibration in the Aether is geometric.

The photon – the smallest entity and the carrier of electromagnetic energy – takes the shape of two tetrahedra.

A free photon has a form of two tetrahedra back-to-back. This shape is also called a triangular dipyramid (or bipyramid).

tetrahedra back to back Rod Johnson triangular bipyramid

Figure by Rod Johnson – Two tetrahedrons joined at a common face to form the “photon” measured by Planck‘s constant

 

A confined photon has a form of a star tetrahedron. The two tetrahedra above have slid together and locked into place.

star tet

 

This has been confirmed by the discovery of the Amplitudehedron by Nima Arkani-Hamed and Jaroslav Trnka and the first image captured of a photon by Radoslaw Chrapkiewicz.

 

 

The Tetrahedron & The Amplitudehedron

The amplitudehedron is the geometry of subatomic particle interactions. Every part is a tetrahedron. It was discovered in 2013 by Nimi Arkani-Hamed and Jaroslav Trnka.

amplitudehedron article

 

“The amplitudehedron is a newly discovered mathematical object resembling a multifaceted jewel in higher dimensions. Encoded in its volume are the most basic features of reality that can be calculated – the probabilities of outcomes of particle interactions.”5

The Amplitudehedron creates the universe in its image. It is a shape that creates amplitudes that jiggle particle tracks in bubble chambers.

It shows the universe is an emanation of a single geometric form.

amplituhedron3 amplitudehedron1

 

The Amplitudehedron appears to be a star tetrahedron. More precisely:  ¼ of a star tetrahedron.

Notice below how the shape can be seen as one corner of the star tetrahedron (Merkaba/Stellated Octahedron).

amplitudehedron2

Credit: David Wilcock

 

 

Verified Shape of the Photon

In 2016 the shape of the photon was independently verified by Polish physicist Dr. Radoslaw Chrapkiewicz.

On July 20, 2016 an article was published entitled, What shape are photons? Quantum holography sheds lightby Cathal O’Connell in Cosmos Magazine.6

The following information is sourced from that article.

photon article

 

Physicists Chrapkiewicz and Banaszek created a hologram of a single light particle (photon).

“The image – which is called a hologram because it holds information on both the photon’s shape and phase – was created by firing two light beams at a beamsplitter, made of calcite crystal, at the same time.”

Each photon could either go straight or turn, depending on the shape of their wave function.

“It’s a little like firing two bullets to glance off one another mid-air and using the deflected trajectories to figure our shape of each projectile.”

After over 2000 repetitions a pattern of flashes built up.

 

They discovered the shape of the photon was a star tetrahedron looked at from its ‘cubic’ angle (on right).

star tetrahedron star angle star tetrahedron cubic angle2

 

It looks exactly like a Maltese cross.

maltesecross 600x600

 

The shape they found (on left) was predicted by Schrodinger’s equation for the quantum wave function (pictured on right below.)

photon shape quantum holography

 

In the arms of the cross where the photons were in step, the image is bright. Where they weren’t, we see darkness.

Therefore, the photon is tetrahedral in nature and appears to be a star tetrahedron.

 

 

Further Info: The Geometry of Light as Tetrahedral in Nature

As we saw in earlier articles, the Vesica is delineated by two equilateral triangles. In 3D they are the back-to-back tetrahedra.

vesica light

 

The length and width of the Vesica form a cross. The cross is the foundation of light.

light8 DM

Credit: Drunvalo Melchizadek, The Ancient Secret of the Flower of Life

 

From One (the Infinite Monad) comes Two (two axes of electricity and magnetism that ‘light and maintain the Central Fire’). From Two comes Four (two positive poles and two negative poles or four directions). From Four comes Eight (the Octave).

This is one aspect of Hermetic wisdom. “I am One who becomes Two; I am Two who becomes Four; I am Four who becomes Eight; I am the One after that.”

The two axes of the cross represent the two axes of electromagnetism.

The long axis, or length is electricity. One end is positive, the other negative.

The short axis, or width is magnetism. Like electricity, one end is positive, the other negative.

A magnetic component is moving at 90 degrees to the electrical component, also in a sine-wave.

 

1024px Electromagnetic waves

 

 

Both components are simultaneously spiraling around each other – rotating in 90-degree segments.

trigonometry trig spiral

 

 

They are in the square root 3 ratio to each other.

vesica sq rt 3

 

 

Light spirals as it moves: every time the Vesica rotates 90 degrees, a new cross is created – the length of the smaller cross becomes the width of the larger cross.

Q 4 sine waves spirals3fresh

 

 

This creates “a geometrical progression of relationships within the Vesica Piscis that identifies the blueprint of light based on the square root of 3.”7

light4 DM

Credit: Drunvalo Melchizadek, The Ancient Secret of the Flower of Life

 

 

 

The Triad in Light & Color

The ability of the human eye to distinguish colors is based upon the varying sensitivity of different cells in the retina to light of different wavelengths.

Humans are trichromatic – the retina contains three types of color receptor cells, or cones.

easy 3298977 1920

 

 

Color is based on threes:

color theory Clay Taylor

Credit: Clay Taylor

 

In light:

Primary colors: red, green, blue-violet.

Secondary colors: cyan, magenta, yellow.

All colors of light together equal white.

The colors are additive, in that they form pure white light.

Direct light adds toward white.

 

In pigment:

Primary colors: red, blue, yellow.

Secondary colors: violet, orange, green.

All colors of pigment mixed together equal black.

 

The colors are reflected, therefore subtractive, in that they remain after direct light colors are absorbed into or subtracted from the surface.

Pigment colors subtract toward black.

Reflected colors of objects show up exactly what the actual color isn’t, since its true colors are absorbed.

What reflects to us is what remains.

The following information is sourced from the brilliant article Light & Color Theory of the Magnetic Spectrum by Clay Taylor.8

clay taylor color sound1

 

 

Additive Color

Additive color is created by mixing a number of different light colors, with shades of red, green and blue being the most common primary colors used in additive color system.

Visible light is a range of EM wavelengths rather than any single one wavelength.

The process of refraction is more extreme for smaller wavelengths than longer wavelengths.

This results in the disassociation and fanning out of what we perceive as the white light into the wavelengths that compose it, which we perceive as separate colors.

When white light is emitted through a prism, three primary wavelengths of color result: red, green, and blue.

When two of these primaries are blended into different combinations they form three secondary colors of: yellow, magenta, and cyan.

additive 15997 1920

 

 

Subtractive Color

Subtractive color explains the mixing of a limited set of dyes, inks, paint pigments or natural colorants to create a wider range of colors, each the result of partially or completely subtracting (absorbing) some wavelengths of light and not others.

When looking at a shadow surrounded by light while looking through a prism, the primary colors appear to be yellow, magenta and cyan.

These seemingly combine to form secondaries of red, green and blue.

circles 27975 1280

 

Cyan = white – red

Yellow = white – blue

Magenta = white – green

Red = blue – green

Blue = green – red

Green = white – blue and red

 

color theory Clay Taylor 2

Credit: Clay Taylor

 

 

Shadows

Shadows are refracted as well.

Shadows are part of the contrast between positive emission and negative absorption of the EM spectrum.

pier 801761 1920

 

When one looks through a prism towards the outside world at a shadow surrounded by light, they will see the shadow refracting in 3 separate bands, just as light does.

The shadows will take on cyan, magenta and yellow hues.

clay taylor shadow

Credit: Clay Taylor

 

 

It All Stems from the 3 Primaries

All emitted colors and saturations possible exist as different ratios of blends between the 3 primary colors of emission.

triad colors2

 

 

All absorbed colors exist as different ratios and blends of the subtractive primaries, which are a result of the negation of a primary color from white.

Additive and subtractive color is actually one and the same.

We perceive colors that are present to perceive, and that depends entirely on which combinations of primary colors are available to resonate with our eyes.

Black is the absence of all 3 primaries.

White is the presence of all 3 primaries.

 

 

Why are there 3 Primary Color/Angles of Refraction in EM Radiation?

Goethe color theory

 

Clay Taylor tells us that magnetism and all its possible energy field arrangements are composed of three irreducible base components.

These are the base triangulation/polarization into:

Positive, negative and neutral.

 

Could this be due to the inherent triangular shape of the photon – the tetrahedron?

triad colors

 

 

 

Light, Color & Sound

Light and color operate on the same harmonic/mathematical principles as sound.

EM spectrum lr

 

Sound operates in the hundreds of vibrations per second.

Light and color operate in the hundreds of trillions of vibrations per second.

 

  1. “All vibration is intimately connected to all other vibration thereby demonstrating:
  2. the interconnectedness of all things and energies
  3. all things are themselves built up from simple vibration to complex chords using universal principles of vibration alone
  4. there is no such thing as chaos in the universe
  5. all things exist by virtue of harmony among vibrations that make it what it is, and
  6. all things are intimately connected by sympathetic vibration.”10

 

“Light, color and sound share the same wave patterns.  What is more, they share the same vibration rates, as J. Dauven proved in 1970.  Diagram A is a composite of both vibrations; sound frequencies (the number of vibrations per second) are shown with a dash-dotted line, and color frequencies are shown with a solid line.  The closeness of the two lines indicates that the experience of harmonious rhythms is shared by the eye and the ear, even though one registers it as color, the other as sound.”

Correspondence between musical sounds and colors.  Sound vibrations of one octave of the keyboard from G to F are tabulated in diagrams A together with the seven spectral colors to show the basic unity in these diverse patterns.  Credit: Gyorgy Doczi – The Power of Limits, 1981

 

 

The Triad in Sound and Music

It takes a combination of only three primary notes (the tone, fourth and fifth) to combine in four secondary ways to produce the 7-note musical scale.

heptad 7 notes

 

 

The ratios 3:2 and 3:1 define the intervals of the fifth and its octave, the most beautiful harmonies other than the octave itself.

heptad circle of fifths

This is the key to all ancient tunings.

 

“The ancients understood our physical world to be a divine mathematical plan, geometry was sacred, number was the fingerprint of life and knowledge of these things was the wisdom of the gods.”11

 

 

The Triangle & Music

Seen below, “If one draws one triangle within another with edges touching [as shown], the side lengths and the circumscribed/ inscribed circles give us the doubling/halving/octave ratio exactly. Continuing the lines of the inner triangle to unite the inscribed and circumscribed circles, we find the golden ratio of phi and 1/phi. This most simple geometric relationship describes how phi is inherent within the triangulation of the fundamental tonic and octave relationship.”12

color sound clay taylor

Credit: Clay Taylor

 

 

Fibonacci is Music

Recall how the Golden Ratio is inherently a part of the Fibonacci Sequence.

1 : 1 : 2 : 3 : 5 : 8 : 13 : 21

“The Fibonacci series is the base of music. Here we have the series going up which breaks into a smooth series of even musical intervals.

When the numbers are going in reverse order we can see the spontaneous generation of odd or enharmonic musical intervals.

The two series will progress to infinity always attempting to form a Harmonic 6th which does not exist in music or nature because the Harmonic 6th signifies perfect unity or harmony or equation of forces. Should this happen the forces then become latent and non-perceptable.”13

 

1 : 1 Unison

3 : 2 Perfect 5th

8 : 5 Minor 6th

21 : 13 Minor 6th

∞ : ∞ Harmonic 6th

34 : 21 Major Sixths

13 : 8 Major Sixths

5 : 3 Major 6th

2 : 1 Octave

 

“It really is a Musical Universe (!) which is both created and evolved from its vibratory root of One demonstrating there is no conflict between concepts of a created universe and theories supporting material evolution. Both these concepts work hand in hand to manifest, choreograph and present the spectacle of beauty, structure, dynamics, utility and love seen all around us.”14

fibonacci lowres

 

 

Keith Critchlow, Triangles and their Musical Significance

See page 219 in The Ancient Secret of the Flower of Life by Drunvalo Melchizadek.

“[Keith Critchlow] drew an equilateral triangle with a line through the middle; then measured to the middle of the center line and drew a line down to the corner and up to the top edge and then vertically down to the center line, as shown. Where that first diagonal line crossed the center line, he then drew a vertical line to the upper edge, then down to the same lower corner. Using the point where it crossed the center line, he repeated what he had done before, then did it once more to the left.”15

Critchlow explains, “Continuing in this way each successive proportion will be the harmonic mean between the previous proportion and the total length, and all these proportions will be musically significant, ½ being the octave, 2/3 being the fifth, 4/5 being the major third, 8/9 being the major tone and 16/17 being the half tone.”

critch1

He is comparing the proportions of these lines to musical tones.

“He then tried measuring it in a different way, starting at a different point of the center line, at ¾, and found that the measurements were 1/7, ¼, 2/5, 4/7, 8/11 and 16/19 – and all these numbers are musically significant.”16

critch2

 

This means “the harmonics of music are somehow related to the proportions of this central line moving through a tetrahedron.”17

triangles music Critchlow2

equalizer 153212 1280

 

 

For clarification on light and color watch: Light, Darkness and Colour: Goethe’s Theory: https://www.youtube.com/watch?v=j6KndO07dVk

and read Light & Color Theory of the Magnetic Spectrum by Clay Taylor: https://www.artofclaytaylor.com/single-post/2016/08/22/The-Magnetic-Spectrum-of-Inertial-Polarization

sculpture 2209152 1920

 

 

  1. Schneider, Michael, A Beginner’s Guide to Constructing the Universe, Harper Perennial, 1994
  2. Critchlow, Keith, The Hidden Geometry of Flowers: Living Rhythms, Form and Number, Floris Books, 2011
  3. http://www.scienceonthenet.eu/content/article/nature-numbers
  4. http://www.meddean.luc.edu/lumen/meded/grossanatomy/threes.html
  5. Wolchover, Natalie, Scientists Discover a Jewel at the Heart of Quantum Physics, 12/11/13, https://www.wired.com/2013/12/amplituhedron-jewel-quantum-physics/
  6. O’Connell, Cathal, What shape are photons? Quantum holography sheds light, 20 July 2016, Cosmos Magazine, https://cosmosmagazine.com/physics/what-shape-is-a-photon
  7. Melchizadek, Drunvalo, ‘The Ancient Secret of the Flower of Life, vol. 2‘, Inner Light Traditions, 1999
  8. Taylor, Clay, Light & Color Theory of the Magnetic Spectrum, 20 November 2016, https://www.artofclaytaylor.com/single-post/2016/08/22/The-Magnetic-Spectrum-of-Inertial-Polarization
  9. ibid.
  10. Pond, Dale, It Really is a Musical Universe! November 1999, http://www.svpvril.com/musicuni.html
  11. Taylor, Clay, A Hint of Rational Unity Among Irrational Constants, 24 November 2017, https://www.artofclaytaylor.com/single-post/2017/11/24/A-Hint-of-Rational-Unity-Among-Irrational-Constants
  12. Taylor, Clay, Light & Color Theory of the Magnetic Spectrum, 20 November 2016, https://www.artofclaytaylor.com/single-post/2016/08/22/The-Magnetic-Spectrum-of-Inertial-Polarization
  13. Pond, Dale, 1993, http://www.svpvril.com/svpweb5.html
  14. Pond, Dale, It Really is a Musical Universe! November 1999, http://www.svpvril.com/musicuni.html
  15. Melchizadek, Drunvalo, ‘The Ancient Secret of the Flower of Life, vol. 2‘, Inner Light Traditions, 1999
  16. ibid.
  17. ibid.

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