Return to Free Library

Return to Science Menu

Previous Article                                                                         Next Article

 

In this article we will move into the geometry of the anatomical structure of the human body.  The golden ratio, just as we saw in plants and animals, is the foundational geometric ratio upon which the human body is built.  As we will see as we move through this series, the golden ratio not only structures the bone lengths of the human body, but it structures many other aspects, both anatomical (structure) and physiological (function).

We will briefly review the golden ratio before we move on to human anatomy.

 

 

The Golden Ratio (Phi)

The golden ratio is the unique ratio such that the ratio of the whole to the larger portion is the same as the ratio of the larger portion to the smaller portion.

This results in a continuous geometric proportion.

 Whole   =   Large Part  = Φ

Large part    small part

 

The golden proportion is expressed as a:b::b:(a+b) or approximately 1.618.

 

No other proportion behaves so elegantly around Unity.

Unity can act as the Greater (whole), mean (longer segment) or the Lesser (short segment). (See below.)

As we have said before, the golden ratio symbolizes how a human being (or other life) can be both a part of the whole and the Whole simultaneously; how one can be both Infinite and finite at the same time.

 

Phi is an irrational (supra-rational) function of number.

It is inexpressible as a simple fraction.

It is seen as a key opening a door to a higher reality of Number.

The golden ratio demonstrates that Number is above all a relationship.

 

Φ = or 1.618033988749894848204586834365638117720309180…

 

φ = 0.61803398875… (pronounced ‘fee’) φ = 1/2(√5-1)

Φ = 1.61803398875… (pronounced ‘fi’) Φ = 1/2(√5+1)

 

Bruce Rawles writes, “It symbolically links each new generation to its ancestors, preserving the continuity of relationship as the means for retracing its lineage.”

“When approaching the subject of the human figure in its relation to the theory of proportion, it would appear that the application of principles must become more difficult, for the figure is symmetrical only if seen exactly in front of rear views. Still in both these cases the progressions of the square and of the equilateral triangle are quite as strongly in evidence as in crystals and symmetrical flowers, and the extreme and mean proportion [phi] occurs again and again throughout the form. The ideal angle and the Egyptian triangle also have their influence in many important places.”1

 

 

Phi in the Human Body

As we have been seeing, “Examination proves that the same law of numbers governs the animate as well as the inanimate world, from the lowest to the highest forms of life.

Examining the human figure, we find, taking the head and chief bones of the skeleton, these numbers in evidence: head, one; mouth, one; nose, one; eyes, two; ears, two. In the body there are arms, two, each containing three bones: the humerus, radius and ulna; legs, two, each divided by three: femur, tibia and fibula; each arm has one hand with carpal group, one, phalanges and digits, five; each leg has one foot, with tarsal group, one, phalanges and toes, five. These are, of course, only certain prominent members and bones, there being many others perhaps equally necessary and certainly equally harmonic.”2

 

As Heraclitus told us, “Man is the measure of all things.”

Randall Carlson says, “The geometry of the cosmos and earth is the geometry of humanity. We are walking embodiments of sacred geometry.”

 

“The height of a well-shaped man is the same as the span of his outstretched arms, these two equal measure yielding a square which encompasses the whole body, while the hands and feet touch a circle centered upon the navel…The [square and circle] combined in the human body suggests in the language of symbolic patterns that we unite within ourselves the diversities of heaven and earth, an idea shared by many mythologies and religions.”

Credit: Gyorgy Doczi – The Power of Limits, 1981

 

The Pentad (5) represents human life or sentient life in general. It also refers to Regeneration.

The Pentad is seen in abundance in the human body: 5 fingers, 5 toes, 5 senses, 5 extremities (2 arms, 2 legs, 1 head).

 

The golden section is derived from 5.  Seen here: Phi = (1 + √5)/2

Five and Phi are inextricably related.

This relationship is found all over the human body – in the proportion of the body, face, legs, arms, etc…

 

Gyorgy Doczi writes, “The diagrams [below of the proportions of the male and female body] show again how all parts of the human body share the same proportional limitations.  Thus, the length relationships of hand to arm to trunk (to the starting point of the spine in the pelvis) are shared, as in the thoroughbred horse, by the relationships of head to neck, trunk, legs, and feet.  The entire human bone structure fits neatly into three golden rectangles and a reciprocal, the latter containing the head.

The unity we share with plants and animals is again visible from the fact that our growth, like theirs, seems to unfold from a single center, which in our case is at the top of the sacrum, just as in the frog.  It may be recalled how the spirals of the daisy and sunflower also unfold from the center.”

 

Credit: Gyorgy Doczi – The Power of Limits, 1981

 

The golden ratio appears thousands of places in the human body:

  • The basic unit is the vertical distance between the brow and the tip of the nose.
  • The distance from the brow the crown is Phi times larger than the brow-nose unit.

Michael Schneider writes, “The brow seems to be a turning point, a plane of reflection.”

The brow is related to the 6th chakra – the 3rd eye – or the energy center representing wisdom being perfectly balanced with compassion.

  • The distance from the nose to the base of the neck.
  • The distance from the neck to the armpit.
  • From the armpit to the navel.
  • From the navel to the reach of the fingertips.
  • From the fingertips to the soles.

Thus, the body is ideally divided into seven phi sections.

To clarify these are:

  1. Crown to brow.
  2. Brow to tip of nose.
  3. Tip of nose to base of neck.
  4. Base of neck to armpit.
  5. Armpit to Navel.
  6. Navel to reach of fingertips.
  7. Reach of fingertips to soles of feet.

 

 

Further Phi Relationships Can be Found:

 

Hands & Feet

  • Three bones of each finger (or toe) are in golden relationship. (Same with all fingers and toes.)
    • Tip to first knuckle
    • First knuckle to second knuckle
    • Second knuckle to third knuckle
    • Third knuckle to space of Destot (divides your cubit (elbow to fingertip) in the golden section).
  • The width of the thumb is also in phi relation to the width of the middle finger.

“The hand is a microcosm mirroring the macrocosm of the body.  It grows out of the wrist as the spine grows out of the sacrum, and as wings grow out of the butterfly, or as leaves and flowers growth out of their stems.”  Credit: Gyorgy Doczi – The Power of Limits, 1981

 

Arms

 

  • The wrist divides the hand and forearm into the golden section.
    • The length of the hand to the length of the lower arm bone has a phi ratio.
    • The length of the lower arm bone to the upper arm bone is also a phi ratio.
  • The width of the forearm is in proportion to the width of the wrist.

 

 

Legs

  • Length of the foot to the lower leg bone is a phi proportion
  • Lower leg bone to the thigh bone is a phi proportion
  • The distance of the knee to calf muscle is in phi proportion to the distance from knee to sole of foot
  • Distance of calf muscle to ankle: distance from calf muscle to sole of foot
  • Distance of mid-thigh to start of kneecap: distance of mid-thigh to end of kneecap
  • The widest part of the thigh is in phi proportion to the narrowest part of the thigh.
  • The width of the leg at the calf is in phi proportion with the width of the ankle.

 

 

Whole Body

  • From feet to head: Where your fingertips touch your sides when arms are hanging loosely to the sides – divides the body into the golden section with the small section on the bottom.
    • This means the distance from the top of the head to the fingertips (φ) is in phi proportion to the distance of the fingertips to the soles of the feet (1).
  • In reverse: with the small section on top, the division point is the navel – this often manifests as whole number Fibonacci approximations such as 5:3 and 8:5.
    • This means the distance from the top of the head to the navel (1) is in phi proportion to the distance from the navel to the soles of the feet (φ).
    • It is common for the female navel to be slightly higher than the golden section.
    • Also common for the male navel to be slightly lower than the golden section.
  • The positioning of the navel falls above and below the golden cut as one grows from ages 17-30.

  • Foot sole to navel: sole to crown of Head
  • Sole to knee: sole to navel
  • Navel to shoulder: navel to crown
  • Navel to mid-thigh: navel to knee
  • navel to mid-chest: navel to base of throat
  • navel to crotch: navel to mid-thigh
  • navel to sternum base: navel to mid-chest
  • A golden ratio also exists between the height and width of the shoulders.

 

See pages 177-183 in Nature’s Harmonic Unity to see the geometric analysis of a male and female body.

 

“As great as the diversities of female and male bodies are, still women and men are united by the almost complete identity of their anatomic proportions, at least as far as the length of their bones are concerned.  The only difference is a general refinement in the measurements of the female skeleton and a widening of pelvic girdle…

A further instance of unity in diversity within human anatomy is the surprising correspondence between proportions of diversely sized bone structures of both sexess.  The figure below shows that all corresponding longitudinal dimensions of tall, average and small women and men tend to fall upon coaxial circles.”

Credit: Gyorgy Doczi – The Power of Limits, 1981

 

Head & Face

  • Length of face to width of face
  • Length of lips to eyebrows: length of nose
  • Length of whole face: length from jaw to eyebrows
  • Length of mouth: width of nose
  • Width of nose: distance between nostrils
  • Width of head at eyes: width of throat
  • Length between pupils: length between the eyebrows
  • Fibonacci numbers in teeth – sum to 13 in each quarter of your mouth over a lifetime.
    • 5 child teeth in each quarter
    • 8 adult teeth in each quarter
  • The two front teeth form a golden rectangle – in a “perfect” smile.

  • Height to width of center two teeth
  • Width of two center teeth to those next to them is phi
  • Ratio of width of smile to third tooth from center is phi

 

  • The head is framed by a golden rectangle; phi proportions mark the eyes, nose, & mouth
  • Base of throat to temple: base of throat to crown
  • Base of throat to earlobe: base of throat to top of ear
  • Brow bone to hairline: brow bone to crown
  • Nose to chin: nose to base of throat

See pages 171 and 173 in Nature’s Harmonic Unity to see the front view and side view of an ‘ideal’ face – in this case the Greek study of Hermes of Praxiteles.  The influence of the pentagon is readily apparent.

 

 

Growth of the body

A baby’s navel is at the body midpoint; its genitals at the golden point.

Adults reverse this: the adult navel is at the golden point; its genitals at the midpoint.

“Thus,” as Robert Lawlor writes, “the position of the navel through human growth is related to the idea of a movement from the dualized, sexualized stance in nature to that of a proportional relation to Unity through the asymmetrical, dynamic power of φ.”

Lawlor adds, “The growth of the human body describes a relation between two generative powers, that of the square root of 2, resulting from halving then doubling, indicated by the location of the sex organs at the body’s midpoint, denoting the quantitatively replicating procreative principle; and that of φ, indicated by the navel, denoting the relational power which integrates the parts with each other and with the all-containing wholeness, as the umbilical point relates the child to its origin – mother universe.”3

 

The baby’s genitals are at the golden point.  This represents the ‘immature’ human’s center as the center of physical evolution, as the genitals represent physical procreation and physical evolution of the species as a whole through the passing on of genes.

 

The adult’s navel is at the golden point.  This represents the ‘mature’ human’s center as the center of spiritual evolution, as the navel represents the 3rd chakra, the seat of self-awareness, courage and willpower.  The 3rd chakra is a springboard to higher levels of spiritual or cosmic awareness.  Inherent in the importance of the 3rd chakra lies ‘the choice’.  The choice refers to a mature human’s ability to focus their will power and actively choose to honor their cosmic natures by making choices each and every day that will propel them to rise to their highest potential for the greatest good.

 

Michael Schneider comments, “The body is a repackaging of the pentagon, another whole in nature’s fabric, with a flavor of the infinite.

The body’s structure is a mirror of our psyche, a denser expression of the energetic patterns of our soul.”4

 

 

Other Phi Ratios and in the Body: The Eye & Ear

 

The Eye

“The progressions of the square apply with equal value to the eye and ear…the progression of the square and the angle of 60° render proportional spaces corresponding to those in normal examples [of the eye].”

This is seen on page 169 of Nature’s Harmonic Unity.

The progressions of the square and triangle (60°) determine the following:

  • The length of the cornea
  • The diameter of the normal pupil
  • The circle of the iris
  • The outer arc of the cornea
  • The position of the entrance to the optic nerve
  • The location of the sclerotic coat and choroid
  • The arcs of the retina

 

“Of course the pupil varies in size, not only in relation to the amount of light it receives but also on account of the temperament of the individual.  In warm temperaments, the pupil is abnormally large, in cold ones it is the reverse, but in the normal or average eye, the proportions of the pupil correspond to the diagram [shown].”5

 

 

The Outer and Inner Ear (Cochlea)

 

Page 170 in Nature’s Harmonic Unity shows that the ear is constructed according to the laws of proportions just as the eye is.

The progression of the triangle (60°) determines the position of the opening of the ear as well as the width of the ear.  The width of the ear is proportional to its length.

Michael Schneider writes, “The shape of the cochlea, the organ that “hears” music, corresponds to how chromatic musical octaves appear when graphed as wavelengths.  Each note is identical to those directly above and below it on the spiral but with a one-octave difference.”6

Schneider adds, “Humans hear approximately ten octaves of sound in a cochlea of two and three quarter spiral turns.”

 

Jeremey Naydler comments on the distinction between the function of the eye and the ear, arguing “that through the reinstatement of listening rather than looking as the basis of our model for relating to the world, it becomes possible for a more open, responsive, and participative relationship with nature to arise.”7

He states in his essay Restitution of the Ear, “What is the deeper meaning of the fact that our modern Western consciousness finds in the visual experience – rather than the experience of touch, taste, smell, or hearing – the one that most closely approximates our experience of thinking and understanding?

For it has not always been so.

Whereas for us the sensory metaphor most often associated with wisdom is ‘far-sightedness,’ implying a practical ability to plan effectively for the future, for the Sumerians the equivalent expression would have been ‘depth of ear’ implying a more contemplative, more inward attunement to the spiritual forces active in the present.

[This concept is present in ancient Egypt as well where] we read:

The fool who does not hear can do nothing at all.

He sees knowledge in ignorance.

The divine gift of hearing is the basis of perception of spiritual truth.

Whereas the eye shows us the surface of things – their extension in space, their form and color – the ear reveals to us that which is hidden from the eye.  The ear, unlike the eye, is physiologically a very internal organ; and what is expressed in sound pertains more to the inner nature of a thing or creature.  The sound that an animal makes gives us an experience of what is happening in its soul, which no amount of looking would communicate to us.

The eye asks us to engage in a practical, instrumental relationship to the world, whereas the ear seems to invite us to overcome our separation from objects that the eye locates ‘out there’ and to involve ourselves with them in a more participative form of knowing.

The eye separates observer from observed where the ear unites them.

Only in the Renaissance did the spectatorial metaphor really come into its own.  The changing relationship is most evident in the scientific revolution, which was a revolution in perception, and whose leading protagonists systematically denigrated all senses other than the eye.

The demand of the spectatorial mentality for exactitude in the observation of natural phenomena led to the exclusion of the nonvisual senses from the new scientific epistemology.

In due course the unquantifiable, nonvisual aspects of our experience became known as ‘secondary’ qualities…In the new scientific worldview, real reality would reveal itself only to the single, color-blind, quantifying eye.

Waking consciousness has become equated in our minds with seeing, for sight is the guarantor of the non-symbolic, surface-reality that our secular culture assumes to be all there is.  But it is not possible in well-lit rooms for conversations to attain the depth of mood they attain by twilight, candlelight or darkness.  When the light is dimmed, when the surfaces of things lose their sharp definitions, then the imagination awakens.

The listening metaphor suggests stillness and a quiet attentiveness.  Whereas the eye is constantly active and mobile, at the heart of the inner ear is the still spiral of the cochlea…If the seeing mind is incessantly busy, the listening mind is still.

I suggest that the cultivation of the art of listening is one of the surest ways of developing a more open, responsive, and contemplative mode of relating to the world.

To look ‘in the mode of listening’ is to look beyond the surfaces of things into that which is expressed through them.  In place of merely noting the external appearance, the listening mind’s eye attunes itself to the interior dimensions of reality, ‘inwardly reading’ that which is concealed from the viewpoint of the detached onlooker.  From being a spectator in the world, even the eye is at least transformed into an organ of participation.”8

 

 

Other Spirals

The shape of the fetus can be overlaid with a Fibonacci spiral.

 

The shape of a curled fist can also be overlaid with a Fibonacci spiral.

 

The pineal gland is found at the center of the golden spiral when a golden spiral is laid against a sagittal cross-section of the brain.

 

The knowledge that the human skeleton is proportioned to the golden ratio is very, very old.  However, it is less well known that the muscular structure is proportioned by spirals, mirroring the spiral structure of DNA. 

 

 

 

Principle of Spiral Arrangement of the Skeletal Muscles of Humans and Animals 

PF Shaprenko and NF Pshenichyi published a paper in 1988 that discusses the spiral arrangement of the skeletal muscles found in humans and animals.9

 

The abstract is as follows:

“It has been stated long ago, that smooth muscle elements in the vascular walls and other tubular systems in the human being and in the animals demonstrate spiral arrangement. The authors decided to show that there is a spiral formation of the skeletal musculature in the human being and in vertebrata at the level of the whole organism, its parts and separate muscles. By means of successive joining certain muscles, their parts and even separate groups of muscular fasciculi by tendons, aponeuroses, fascia and intermuscular septa, ligaments and bones kinematic chains of muscles have been revealed, those chains that have spiral direction regarding the longitudinal axes of the body and its parts.

Two examples of left- and right-hand-screw types of spirals are presented and it is stressed that the spiral principle reflects biological symmetry of structural oppositions–enantiomorphism. A conclusion is made that the spiral form of the skeletal musculature is a universal regularity for the human being and for all vertebrata. The cylindric form of the vertebral body serves as a predestinated moment for this. The spiral twisting of the muscles is the most optimal for ensuring variability of movements and performing adaptive survival of the human being and animals in the Earth gravitational field.

In 1950 Raymond Dart published a paper entitled: Voluntary Musculature in the Human Body; The Double-Spiral Arrangement in the British Journal of Physical Medicine.10

Dart tells us, “The double-spiral arrangement of the voluntary musculature is basic.  In ontogeny, as in phylogeny, man grows and moves spirally.”

[Note: ontogeny is about the development of an individual.  Phylogeny is about the evolutionary history of a population and how it is related to others.]

 

Carol Porter McCullough writes, “Anatomists have traditionally divided the musculature into various muscle groups.  This is useful for identification purposes but not useful for understanding the working whole of human movement.”

Dart writes in his paper, “The spirals of the human musculature are mirror images of each other.  Designating the right side of the pelvis as a starting point, the muscle sheet of one of the spirals travels diagonally around the side of the torso, crossing over the front mid-section to wrap diagonally upward to the left side of the torso, where the road of muscle make a “Y”, one avenue junctioning with the muscles of the left arm, the other avenue snaking its way diagonally across the back, continuing on its diagonal journey across the neck to hook onto the head behind the ear in its original hemisphere of the right side.”

 

Anatomist Tom Myers defines the spiral line based on Dart’s work:

“The spiral line loops around the body in a double helix, joining each side of the skull across the upper back to the opposite shoulder, and then around the ribs to cross in front at the level of the navel to the same hip.  From the hip, the spiral line passes like a ‘jump rope’ along the anterolateral thigh and shin to the medial longitudinal arch, passing under the foot and running up the back and outside of the leg to the ischium and into the erector myofascia to end very close to where it started on the skull.”

Conclusion

In this article we see very clearly how the golden ratio is embedded within human anatomy.

The entire human body is formed upon a matrix of geometry which includes the icosahedron/dodecahedron and their foundational proportion, the golden ratio.

We also see how the human body musculature system is wrapped around the body in a double helix spiral mirroring DNA and many other natural spirals found in nature.

 

In the next article we will look deeper into other aspects of the human body, finding how the golden ratio and other geometry fit in.

 

 

  1. Colman, Samuel, Nature’s Harmonic Unity: A Treatise on its Relation to Proportional Form, Forgotten Books, 2017
  2. ibid.
  3. Lawlor, Robert, Sacred Geometry: Philosophy & Practice, Thames & Hudson, 1982
  4. Schneider, Michael, A Beginner’s Guide to Constructing the Universe: The Mathematical Archetypes of Nature, A Voyage from 1 to 10, HarperCollins, 1994
  5. Colman, Samuel, Nature’s Harmonic Unity: A Treatise on its Relation to Proportional Form, Forgotten Books, 2017
  6. Schneider, Michael, A Beginner’s Guide to Constructing the Universe: The Mathematical Archetypes of Nature, A Voyage from 1 to 10, HarperCollins, 1994
  7. Naydler, Jeremy, The Future of the Ancient World: Essays on the History of Consciousness, Inner Traditions, 2009
  8. ibid.
  9. Shaparenko PF, Pshenichnyi NF; Principle of Spiral Arrangement of the Skeletal Muscles of Humans and Animals, June 1988, https://www.ncbi.nlm.nih.gov/pubmed/3190472
  10. Dart, Raymond, Voluntary Musculature in the Human Body; The Double-Spiral Arrangement, British Journal of Physical Medicine, Dec 1950, http://www.alexandercenter.com/dartspirals.html

 

Return to Free Library

Return to Science Menu

Previous Article                                                                         Next Article