What is Sacred Geometry and why should we know about it? Children taught about the principles of Sacred Geometry will use this information to inform all of their creations, ultimately creating a more beautiful and balanced world.
What it is and a case for
why it should be included
in elementary education
By Eileen McKusick
Better Living Through Geometry
“There is a pattern in the heavens,
where those who want to can see it,
and establish it in their own minds.”
“Geometry existed before the creation.”
“No state can find happiness unless the
artist drawing it uses a divine pattern.”
Sacred Geometry- What is it?
• Sacred Geometry is the blueprint of the natural
world and the basis of all form.
• It is an ancient science that explores and
explains the energy patterns that create and
unify all things and reveals the precise way that
the energy of the Universe organizes itself.
• On every scale, every natural pattern of growth
or movement conforms inevitably to one or
more geometric shapes.
What makes it “Sacred”?
(and isn’t that a bad word in our secular culture?“)
• Sacred means ‘holy’ or spiritual, a term left by science to
religion- meaning it has no place in a secular education.
• Secular mathematics is what is taught in school- a focus on
the quantity aspect of numbers (that turns children into
‘pocket calculators’) and gives no attention to the
underlying connection of numbers and geometry to
nature, the universe, or the human psyche.
• Geometry and numbers are sacred because they codify the
hidden order behind creation
• This lack of awareness of underlying connective orderly
patterns creates a cosmology or universal perception of
What makes is Sacred (con’t)
“Symbolic and sacred mathematics encode subtle
experiences whose purpose is different from secular
math. They can invigorate, refine and elevate us to
discover the inherent proportion, balance , and
harmony in the patterns that construct the universe
The ancients believed that the experience of Sacred
Geometry was essential to the education of the soul.
They knew that these patterns and codes were
symbolic of our own inner realm and the subtle
structure of awareness”.
“man is the measure of all things”
“Official” Contemporary Perspective
• “A contemporary usage of the term sacred
geometry describes assertions of a
mathematical order to the intrinsic nature of
the universe. Scientists see the same
geometric and mathematical patterns as
arising directly from natural principles.”
??? What is the difference???
Patterns, patterns, everywhere
• Everything has a pattern,
and that pattern is the
key to creating a specific
effect – these patterns
create everything in the
• So, what are the patterns
and where do we see
them? And what do they
A voyage from 1-10
• Next we will look at each of the numbers from
• Each number was seen as expressing an
archetype of nature
• “the original ten patents for designs found
throughout the universe”
• Tells the story of Creation from the
perspective of a geometer.
One- The Monad
The number 1 is symbolized by the circle- the shape from
which all other shapes ariseIt breathes into the void and gives rise to all other numbers
111111111 x 111111111= 12345678987654321
The area within the circumference which manifests between nothingness –
the zero point inside- and everything – the infinite points around the
Nothing exists without a center around which it revolves. When the center
does not hold, the entire affair collapses.
When something is pointless, it has no center holding it together.
• This is a symbol
representing the monad,
or one, that has arisen on
• The eternal unity of all
• The cycle of endless
• Universe: One Turn
The marriage of two circles gives birth to
Also the overlapping space between the
two circles is known as the vesica piscis or
From this womb, the rest of the numbers
and their respective shapes emerge.
•The principle of the dyad is polarity
•The paradox is that opposite poles remember their source and attract
each other in an attempt to merge and return to a state of unity
•Dyad simultaneously divides and unites, attracts and repels, separates
from unity and craves to return to it.
•A line creates both a boundary that divides and a line that binds.
It takes two to tango
• Only by acknowledging both poles in the
pair as inseparable can we overcome
duality and get to their common source
in the monad. In our deepest self, we are
beyond all polarity.
• For anything to manifest, however, there must be polarity.
• Monad and Dyad were considered to be the parents of
numbers. Dyad is the doorway between the one and the
• Hydrogen, the first atom to emerge, has a positively
charged proton and a negatively charged electron. It is the
door between the unknown unity (monad) and the
subsequent elements, which are built by fusing hydrogen.
Triad- the firstborn- Triangle is the
first shape to emerge from the
•Natural to divide a whole into three parts : Beginning,
middle and end
•An inherent tripartite wholeness of the universe
•Trinity- tri-unity – three as one. Triangle- preeminent symbol of
•Opposites are balanced by a 3rd mediating element
•Ancient mathematical philosophers referred to the triad as
prudence, wisdom, piety, friendship, peace, harmony, unanimity,
•Fundamental structures of the world are braced by triangles- a
triangle is self-sufficient: it encloses the smallest area with the
A lesson from the triad
Two forces can be opposites without resolution, like lawyers
without a judge- but introduce a properly chosen third
factor and it can induce a relationship that unifies them and
brings them to a whole new level. A minimum of three
elements is required to weave into a whole (think of a
braid)- the principle of the triad can teach us how to
resolve conflict. No enduring resolution of any kind is
possible without three aspects, two opposites and a
neutral, binding, balancing, arbitrating presence (think
executive, legislative, judicial). Knowing how to choose the
third factor means the difference between a conflict’s
resolution and its perpetuation. The third element, which,
if chosen properly achieves a previously unknown level of
balance and completion.
The square, cube, and three dimensional
space emerge from the vesica piscis next
•4-ness/square associated with the earth – solid, stable earth
•4 directions 4 winds 4 seasons 4 corners of the globe
• 4 footed creatures are earthbound
•Mater- Latin for Mother – Matter
•Pater- Latin for Father- Pattern
•Natural forms arise from mating of pattern and matter
•The arising of these natural patterns in 3-D where they can be
clothed in the four states of matter
•4 elements or states of matter•Solid, liquid, gas, plasma / earth, water, air, fire
The five Platonic Solids or
• Fall in the domain of the number 4 because this is the birth
• These are Forms that fit perfectly within a sphere
connected by identically shaped surfaces, edge lengths, and
angles – an identical view in all directions
Dodecahedron: Heaven above
Hexahedron (cube): Earth/Solid
Classical view of these shapes
• The Greeks taught that these five solids were the
core patterns of physical creation.
• Four of the solids were seen as the archetypal patterns
behind the four elements (earth, air, fire, and water)
• The fifth was held to be the pattern behind the life
force itself, the Greeks' ether. This fifth solid, the
dodecahedron, was in fact kept a closely guarded
secret in the Greek school of Pythagoras and even
Plato spoke little of it
• They feared that this pattern could cause tremendous
destruction if misused.
• The aether energy can arrange itself into basic
geometrical wave patterns that were named after
Plato, the Platonic solids to form matter. Almost
2,500 years ago, Plato wrote that the physical
world was constructed from the Platonic solids.
The Platonic solids arrange themselves in what
chaos theory calls fractal patterns weaving a
matrix in space interconnecting atoms with the
stars. The scales of the Platonic solid shapes are
different but the ratios between them are still the
same (following the Hermetic principle as above
The introduction of life itself Pentagonal symmetry is the supreme
symbol of life, universally appealing
•Quintessence- the life that infuses the four elements that they
cannot create on their own
•Stardom conveys a deep seated association with excellence and
brilliance and power.
•Pentagons abound in the animal and plant kingdoms
•Flower of every edible fruit has five petals
•Seeds, holders of life itself, arranged in a star pattern in fruit
•Look at leaves, flowers, fruits – see the invisible energy web of
the archetype made visible as a pattern of living cells.
•Pentad holds the principles of the geometry of regeneration.
Regenerates within and without.
The Fibonacci Series
• Fibonacci series begins with two “terms”
• Zero plus unity, nothing and everything, the unknowable
and the manifest monad
• To find each next term, just add the latest two terms
together. This produces an endless series:
• 0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610 …
• Series grows by accruing terms that have come from within
itself, from its immediate past
• Each term may be traced back to its beginning as unity in
the monad which itself arose from the “incomprehensible
mystery of zero”
• The average number of petals on each type of flower will
be Fibonacci numbers, same with pine needle clusters.
• Divide each fraction by the term before it:
…8/5, 13/8, 21/13, 34/21, 55/34, 89/55…
• And the numbers get closer and closer to
1.6180339… or Phi
• The Golden Mean, golden ratio, divine proportion,
golden cut, etc : the ideal balance in life
• Phi is a greek letter and it was named as such in
this last century to honor Greek sculptor Phidias
who used it to proportion his designs, from the
Parthenon to the famous statue of Zeus
• The purest expression of moving energy.
• The universe moves and transforms in spirals, never in
straight lines – for example, plant growth
• Clashing opposites resolve in spiral balance – balance in
motion made visible
• Archimedian spiral, like a coiled rope or Fibonacci spiral
• Spirals have a calm eye that corresponds to zero at the
beginning of the Fibonacci sequence.
• Calm eye is the unmanifest, spiral is the manifest
• Without the eye there would be no spiral expansion or
dissolution, no whirling, no balance, no life
• Calm center exists within all living things, including self- not
as a concept but as an actual part of the pattern and
dynamic process that is “Self”.
More about spirals
• Spirals grow by
and shrink by dissolution
• Matter precipitates where positive and negative
spiral rhythms synchronize.
• Energetic lines of force that the more dense
substance of the “world mother goddess” or
“mater” precipitates- descending from light
(plasma) to gas to liquid to finally solid
Fractals- “as above, so below”
The repetitive patterns of the Platonic solids that fit into each other are fractals. A fractal is a
repetitive pattern that can be scaled to any size. The scale may change but the ratio is held
Now the fractal patterns that shape the atom, according to Daniel Winter also shape our planets
and stars, in fact the universe.
A fractal has self-similarity at all scales, it’s the same geometric pattern repeated. The inner
structure in a fractal is reflected in the outer structure. Fractal means fraction of the all, indicating
that each piece is part of the whole. It is the basic idea of a hologram and this is why according to
Daniel Winter the universe at large is just a super-hologram. The fractals of electromagnetic energy
interconnect everything with everything within the universe and are the basic building blocks of
this hologram. The fractal repetitive structures of electromagnetic energy weave a giant cobweb
throughout the universe.
The wavelengths of planets and stars are huge in comparison with the wavelengths of the atom,
however when their wavelengths fit into the Fibonacci sequence of the Golden Mean, they
interfere non-destructively; they implode and form a fractal attractor that we call gravity! This is
how the planets and stars are connected by means of imploding electromagnetic waves that we
experience as gravity.
So if the universe is in essence a hologram and there is only one principle that shapes everything
from atoms to planets, stars, and the universe at large, we should find proof of these vortexes,
Platonic Solids, and doughnut structures in all parts of the universe.
• 6 days of activity around a central day of rest
• Hexagram star- Seal of Solomon/Shield of David/Mark of Vishnu
• Hexagon works in situations requiring strength and stability (hex
nuts, for example)
• Best use of material with the least amount of weight : in beehives1.5 ounces of wax holds 4 pounds of honey!
• Circles and the hexagons formed by them are said to tessellate
• Hexagonal tessellation recurs endlessly in nature and in the
human body – lungs muscles the eye and more
• Six sided forms in nature are often non-living – ie. snowflakes
• 3 corner 120 degree joints- common in the
realm of molecules and crystals
• Quartz is ordered, timekeeper
Twelve- Six doubled
• Dodecagon- Twelve – The framework
number – used in teepees and lodges in
native Americans and other societal structures
• Sunlight- the sun king – surrounded by 12Jesus, King Arthur and others
• 12 constellations of the zodiac 12 part epic myths
12 step programs 12 disciples 12 tribes of Israel
12 notes in the chromatic musical scale
Acupuncture- 12 meridians around one central channel
• weights and measures exhibit 12-ness - Metric system
makes calculations easy but dissociates us from a
framework system linked with the cosmos.
• 12 around one within our deeper psyche
• The heptagon cannot be born through the vesica piscis – it cannot
be constructed by the compass, straight edge and pencil accurately.
• Cannot be entered (divided) and cannot produce other numbers
within the decad- this is why it is considered a virgin or holy
• Nature does not produce heptagons – nothing in the mineral world
is 7 sided
• 7 creates a familiar rhythm- days of the week, notes in the musical
scale, 7 years til every cell in the body is replaced, information stays
on your credit report for 7 years.
• Temples to Athena, who sprang from the head of Zeus, were
designed and constructed around the number 7
• 7 chakras – white light prisms through the body to separate out
into these energy centers like the colors of the rainbow.
• 7 sets of endocrine glands
7 and 12 in music and elsewhere
• 7 notes in scale plus 5 sharps/flats = 12 note chromatic scale
• Musical scale was designed to play the harmonies of the heavens,
the music of the spheres, allowing higher principles to enter our
lives through our sense of hearing and emotion.
• Music was seen as having great power for producing heaven on
• Music bypasses the intellect with the power to manipulate
passions and emotion- in this way, music was used to heal.
• Ancients sought to tune or purify themselves so that the unseen
divinity deep within them could better play upon their instrument
in the world.
• “We are the 7 stringed lyre of Apollo, whose music is heard by
both god and humans”
• 12 has relations with all the numbers in the decad, 7 has none
• Hidden, unborn, eternally elusive side of 12 but they are often
together (12 meridians, 7 chakras)
7 notes/centers in the body
•7 chakras – white light prisms through the body to separate
out into these energy centers like the colors of the rainbow.
•Correspond to the 7 sets of endocrine glands
Octave- brings you back to the beginning
Chess 8x8 I Ching 8x8
Peace and Stability
Also relates to the moon
Octad displays wholeness, cycles, polarity
and manifestation as the doubling of 4
• Mitosis- 8 step process
• Of particular significance and symbolism in
Nine - Ennead
•3x3 x3 trinities
•The ultimate expression of something
•Whole nine yards- go all the way
•Dressed to the nines
•Nine innings in baseball
•Nine months gestation
•Nine justices in the supreme court
•Boundary between mundane and infinite
•All encompassing perfection
•Completion of a journey and a return to the origin
•A journey into limitlessness
•Two parent 1-2 7 children 3-9 Portrait of a whole
family of numbers gathered together
•Comprehends and harmonizes all numbers below it
•Generative power to the infinite
•Fulfillment- new beginnings
In Education • At every scale of existence, from
the subatomic to the galactic, the
same key patterns bring all things
• These patterns can easily be taught to and shared with
children – in doing so, we foster in them an awareness
of the underlying patterns and harmony inherent in the
• This can be a key component in creating a more
balanced and harmonious future.
• “Better living through geometry”
• (maybe we can call it “classic geometry“)
• Bangs, Herbert. The Return of Sacred Architecture: The Golden Ratio
and the End of Modernism. Inner Traditions, Vermont, 2007
• Doczi, Gyorgy. The Power of Limits: Proportional Harmonies in
Nature, Art and Architecture. Shambhala, Boston, 2005.
• Ghyka, Matila. The Geometry of Art and Life. Dover Books, New
• Michell, John. How the World is Made: the Story of Creation
According to Sacred Geometry. Inner Traditions, Vermont, 2009
• Michell, John. The Dimensions of Paradise: Sacred Geometry,
Ancient Science, and the Heavenly Order on Earth. Inner Traditions,
• Schneider, Michael S. A Beginner’s Guide to Constructing the
Universe. Harper, New York, 1994.
• Skinner, Stephen. Sacred Geometry: Deciphering the Code. Sterling
Publishing, New York, 2006.