In the field of sacred geometry, the torus is a three-dimensional shape that has intriguing symbolic meanings in spirituality, culture, art, architecture, and science. Furthermore, it’s a shape that appears throughout our natural world. In this post, we’ll explore the torus in sacred geometry and how it appears in many aspects of our lives.
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A torus is a three-dimensional geometric shape that resembles a donut, a life preserver ring, or a tire inner tube. The name is derived from Latin, in which it means a circular pillow, a strong rope, or a muscle.1
When illustrated, the torus appears like a revolving circle in three-dimensional space that’s revolving around an axis that is coplanar with the circle. Coplanar means two or more points, or lines, lie on a common plane. So, the torus has two radiuses – a large one and a small one.
On a symbolic level, a torus implies motion in a continuous cycle. In addition, because a torus has two radiuses – a large one and a small one – it represents the idea of something small that is an integral part of something larger. Hence, the torus has a number of symbolic associations. For example, here are some concepts that the torus symbolizes:
The torus shape is often depicted in three distinct forms: the ring torus, the horn torus, and the spindle torus. In addition, a fourth type is named for the mathematician William Clifford. Here’s a description of each one and what they symbolize:
A ring torus is the classic donut-shaped torus, with a hole in the center. The ring torus represents a cycle, unity, and interconnectedness. The central hole may symbolize emptiness, potential, or the infinite within the finite.
A horn torus is formed by revolving a convex curve (like a parabola) around an axis, creating a toroidal shape with a horn-like appearance on the interior. It is often associated with growth, expansion, and evolution. The spiraling nature of the horn torus suggests continuous development and progress, symbolizing a journey or the path towards greater understanding and enlightenment.
A spindle torus, also known as a spindown torus, is formed by revolving a concave curve (like a hyperbola) around an axis. It resembles a spool or a spinning top. The spindle torus represents the convergence of energies, concentration, and focus. It symbolizes gathering and integrating various elements or forces towards a central point, signifying the process of concentration and unification of purpose or intention.
A Clifford torus is donut-shaped like the ring torus. However, it appears squished or slightly flattened. The shape helps mathematicians and scientists understand how different shapes and spaces can be related to each other or transformed. This version of the torus is named for the mathematician William Clifford, who made significant contributions to the field of geometry.
Mathematicians define the torus shape with parametric equations, including geometric formulas. Understanding of the torus’ mathematical properties is useful in the fields of geometry, topology, algebra, and physics. Its unique structure and properties make it an intriguing object of study that has numerous applications in math and science.
In fact, the torus shape appears in physics in various ways and it has significant implications when it comes to understanding fundamental principles of the Universe. For example, the torus form appears in magnetic fields, quantum physics, fluid dynamics, the study of black holes, energy flow, and even the structure of the Universe.
In one scientific theory, the Universe is in a state of expansion. For example, the Big Bang Theory describes the Universe as having started very small and then expanding rapidly in an explosive manner.
Other theories say the Universe is in a state of perpetual expansion and contraction. The Toroidal Universe Theory is one way of describing this phenomenon. It speculates that the Universe is not actually expanding; it just appears that way because space and time are “flowing” through the Universe dynamically in the shape of a torus.
Thus, this theory proposes that the Universe is simultaneously expanding and contracting in a closed loop – “stretching at the top where space-time emerges from the center of the torus, and contracting at the bottom where space-time flows back into its center,” writes Lee Bladon, a consciousness researcher and author. “The Toroidal Universe Theory also explains why time only flows in the one direction – forwards!” he writes.2
As is the case with other sacred geometry shapes, the torus appears in many ways throughout our natural world. Here are some examples:
Sometimes referred to casually as “cosmic donuts,” groups of galaxies can clump together in toroidal, or ring-like, shapes. This happens because of the way gravity (and complex interactions between galaxies and dark matter) pulls them together and causes them to gather around a center, forming a donut-like structure.3
Lenticular clouds also have a toroidal, or lens-like, shape. They form in the atmosphere, typically near mountain ranges or other geographical features that disrupt air currents, which creates their shape.
Tornadoes can also have a toroidal appearance. The funnel cloud of a tornado resembles a hollow, elongated torus with a strong rotating airflow.
Gyres in the ocean and whirlpools in other bodies of water can exhibit toroidal patterns due to the Earth’s rotation and other natural forces.
Reef bubbles are circular, toroidal air or gas pockets that form underwater, often near coral reefs. (SCUBA divers can cause them too as they exhale.) Their toroidal shape results from the dynamics of gas rising up and encountering resistance from the surrounding water, which forms the gas bubble into a rounded, donut-like shape.
Certain species of anemone have toroidal, or ring-shaped, structures Their distinct torus shape is how they absorb nutrients while it also provides protection and structural stability.
Pumpkins, tomatoes, apples, and bell peppers are all examples of produce that have the shape of a spindle torus.
Each year, a new layer of growth is added in a tree, which creates concentric circles that resemble the structure of a torus.
The eye spot pattern on the wings of some butterfly and moth species can appear like the shape of a torus.
Under a microscope, red blood cells that are packed closely together can appear like little donuts. The toroidal pattern helps red blood cells move efficiently through the bloodstream.
As we breathe in and out, even our own respiratory system displays a toroidal pattern.
The human heart, which some describe as the “seat of the soul” also created toroidal energy patterns as it pumps blood through the body.
For those who believe in sacred geometry, the torus shape’s prevalence in nature underscores how everything, including our own bodies, is integrally connected with the greater Universe.
As art reflects our perception of the natural world, the torus has appeared throughout art for centuries.
One example of the torus in art is the mandala, which is an intricate, circular artistic design. Mandalas are spiritual symbols and a sacred art form. In fact, the term “mandala” is derived from the Sanskrit word for “circle” or “center.” Mandalas typically have a circular or toroidal design and are used in various spiritual traditions for meditation, contemplation, and focusing the mind.
The sacred geometry artist Janette Oakman incorporates the torus and other sacred geometry shapes into much of her work. In this video, she provides a demonstration of to draw a torus with simple geometry tools:
The artist Anish Kapoor is famous for his large-scale sculpture entitled “Cloud Gate,” which is located in Millennium Park in Chicago. Also referred to as “The Bean,” the stainless steel sculpture is torus-shaped.
If you’re familiar with how potters “throw”clay using a pottery wheel, they often create toroidal shapes before turning the clay into a cup, bowl, or even a ceramic sculpture.
For centuries, architects have also incorporated toroidal elements into their designs, including in building facades and arches. The torus shape’s elegant and harmonious form lends itself well to creating peaceful spaces. Here are some examples of the torus in architecture.
In Gothic architecture, ribbed vaults are a key element that often takes on a toroidal form. The ribbed vaults form a network of intersecting arches and ribs, creating a series of curved, torus-like structures that support the weight of the ceiling and distribute it down the columns and pillars. Architects can make the ribs rounded or pointed, which contributes to the overall aesthetics and structure of the vaulted ceiling.
In classical architecture, particularly ancient Greek and Roman styles, column bases often feature torus shapes. The base of a column has a toroidal form, which provides a transition between the column and the supporting surface.
In Romanesque architecture, you can find torus-shaped moldings along arcades and archways. These moldings, known as torus moldings, often have a rounded, semi-circular cross-section and are used to add decorative as well as structural elements to arches and walls.
In ancient and modern times, colosseums take on a toroidal shape, reflecting a focal point emitting energy (the sports team, entertainer, etc.) and a circular perimeter (the audience) absorbing the energy and then giving it back.
Balusters in Renaissance and Baroque architecture frequently incorporate a toroidal form. The baluster’s shape, with its rounded central section resembling a torus, provides both aesthetic appeal and structural support for staircases, balconies, and railings.
Islamic architecture often employs intricate geometric patterns, some of which incorporate toroidal shapes. These patterns can be found in tile work, muqarnas (which are honeycomb-like decorative elements), and other decorative features throughout Islamic buildings.
Some contemporary architects draw inspiration from the torus shape for entire building designs, such as round homes with center courtyards.
In addition, the torus shape appears in contemporary architectural detailing and ornamentation, such as handrails, lighting fixtures, and furniture design.
As with art and architecture, the torus shape is a symbol that appears in different cultures and religious beliefs. Here are some examples:
As mentioned above, torus shapes appear in Hindu and Buddhist mandalas. The circular mandala represents the Universe and the idea that all beings are interconnected and part of a larger cosmic whole. Meditating on the toroidal pattern of the mandala can aid in spiritual growth, balance, and ultimately enlightenment.
In Hinduism, the chakras are energy centers in the body. You can envision them as toroidal wheels, or vortexes of energy. The toroidal representation emphasizes the flow and balance of energy within your body.
stupa, which means “heap” in Sanskrit, is a sepulchral monument, a place of burial, or a receptacle for religious objects. Ancient stupas held portions of Buddha’s ashes, which energized the mound.4 These stupas also have a torus-like shape.
The ankh, an ancient Egyptian symbol, resembles a cross with a loop at the top, which resembles a torus shape. The ankh represents life, immortality, and the eternal cycle of life, death, and rebirth. The loop at the top represents the eternal and cyclical nature of existence.
For Native Americans, the medicine wheel holds important spiritual significance. The medicine wheel can also take on a toroidal shape. The medicine wheel represents the interconnectedness of all life, the four cardinal directions, and various aspects of existence, such as the seasons and stages of life.
In Christianity and other spiritual faiths, halos and auras have torus-like shapes. These shapes symbolize divine energy, or light emanating from an individual, which signifies a high spiritual consciousness or spiritual enlightenment.
Also in Christianity, the Holy Grail is sometimes described as a torus.
The premise is that the torus shape is the result of a sphere in which a vortex opens up at the top and the bottom, creating a channel that goes through it. The energy flow moving through (or circulating through) the torus maintains the structural integrity of the original sphere, despite there being a vortex, or channel, through it.
This open channel matches the geometry of what is called a double vortex: It’s widest at the outer boundaries then narrow at the center of the sphere. The result is an hourglass shape within the sphere.
The geometric name for this is a hyperbola. A hyperbola is formed when two vortexes meet at their tips. This is like two cones joined together at their points.
If you visualize it, this is the shape of a grail.5
This is a profound idea in many ways. While the Holy Grail is not mentioned specifically in the Bible, by many accounts, it was the chalice for the wine that Jesus shared with his apostles at the Last Supper. As the story goes, Jesus told his apostles that the wine represented his own blood. By other accounts, the Grail was used to collect Jesus’ blood when he was crucified.
In either case, the Grail represents Jesus. So, from the symbolic perspective of sacred geometry, the Grail as a torus signifies a vessel through which divine energy courses through without compromising its structure. In essence, this is exactly who and what Jesus was: a vessel for God’s divine energy. (We’ll go into this idea more in the section of Spirituality below.)
The Aztec calendar stone, also known as the sun stone, features a circular design with a toroidal shape at its center. The stone symbolized the cyclical nature of time, life, the seasons, and the sun for the ancient Aztecs.
Ancient stone circles, such as at Stonehenge in the UK or the Drombeg Stone Circle in Ireland, feature toroidal, or circular, layouts of standing stones. Archeologists believe these mysterious prehistoric monuments served as astronomical observatories. People of ancient cultures used them to track celestial events, integrating them into their spiritual ceremonies.
In conjunction with the concepts illustrated above, here’s what the torus can symbolize on a personal and spiritual level:
Unity and wholeness – The torus represents the interconnection of all life and matter in the Universe. It reflects the idea that we are all connected and are part of a larger, unified whole.
Cycles and continuity – The torus’ circular and continuous form symbolizes cycles and continuity. It represents the eternal nature of the seasons and time as well as life, death, and rebirth. It also symbolizes the never-ending process of creation, transformation, and regeneration.
Energy flow – The torus also represents the idea that everything is energy and that energy is in flow. We are all energy and how we use and direct that energy has an effect on everything around us.
Balance and harmony – With its fluid and yet symmetrical shape, the torus symbolizes harmony and equilibrium. It represents finding balance between opposing forces, or energies, achieving inner peace, and living in harmony within one’s self and the greater Universe.
Creation and manifestation – The torus is also a symbol of creation and manifestation. It represents the process of bringing ideas and intentions from the inner realm (the center) to the outer world (the surface), transforming thoughts into reality.
Protection and healing – In some spiritual practices, the torus serves as a protective and healing energy channel. Your own body can be described as a grail cup or a vessel for divine energy to flow into it and through it.
Thus, visualizing and working with the torus shape can enhance your own energetic field, promoting spiritual protection, healing, and balance. It can also enable you to radiate out this kind of positive, loving energy.
Soul and divine presence – As with your physical body, the torus also represents the divine presence of your soul within you. The center of the torus symbolizes the soul or the essence of one’s being, which radiates outwards to express itself in the external world.
In the realm of sacred geometry, the torus shape holds profound symbolism. It embodies the interconnectedness within the tapestry of life on Earth and our profound link to universal energy. As a ubiquitous symbol, it encapsulates the idea that we are all an integral part of something magnificent.
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