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Sacred geometry ascribes symbolic and sacred meanings to certain geometric shapes and certain geometric proportions. [1] It is associated with the belief of a divine creator of the universal geometer. The geometry used in the design and construction of religious structures such as churches, temples, mosques, religious monuments, altars, and tabernacles has sometimes been considered sacred. The concept applies also to sacred spaces such as temenoi, sacred groves, village greens, pagodas and holy wells, Mandala Gardens and the creation of religious and spiritual art.
The belief that a god created the universe according to a geometric plan has ancient origins. Plutarch attributed the belief to Plato, writing that "Plato said God geometrizes continually" (Convivialium disputationum, liber 8,2). In modern times, the mathematician Carl Friedrich Gauss adapted this quote, saying "God arithmetizes". [2]
Johannes Kepler (1571–1630) believed in the geometric underpinnings of the cosmos. [3] Harvard mathematician Shing-Tung Yau expressed a belief in the centrality of geometry in 2010: "Lest one conclude that geometry is little more than a well-calibrated ruler – and this is no knock against the ruler, which happens to be a technology I admire – geometry is one of the main avenues available to us for probing the universe. Physics and cosmology have been, almost by definition, absolutely crucial for making sense of the universe. Geometry's role in this may be less obvious, but is equally vital. I would go so far as to say that geometry not only deserves a place at the table alongside physics and cosmology, but in many ways, it is the table." [4]
According to Stephen Skinner, the study of sacred geometry has its roots in the study of nature, and the mathematical principles at work therein. [5] 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 sometimes interpreted in terms of sacred geometry and considered to be further proof of the natural significance of geometric forms.
Geometric ratios, and geometric figures were often employed in the designs of ancient 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. Mandala Vaatikas or Sacred Gardens were designed using the same principles.
Many of the sacred geometry principles of the human body and of ancient architecture were compiled into the Vitruvian Man drawing by Leonardo da Vinci. The latter drawing was itself based on the much older writings of the Roman architect Vitruvius.
Mandalas are made up of a compilation of geometric shapes. In Buddhism, it is made up of concentric circles and squares that are equally placed from the center. Located within the geometric configurations are deities or suggestions of the deity, such as in the form of a symbol. [6] This is because Buddhists believe that deities can actually manifest inside the mandala. [7] Mandalas can be created with a variety of mediums. Tibetan Buddhists create mandalas out of sand that are then ritually destroyed. In order to create the mandala, two lines are first drawn on a predetermined grid. [6] The lines, known as Brahman lines, must overlap at the precisely calculated center of the grid. The mandala is then divided into thirteen equal parts not by a mathematical calculation, but through trial and error. [7] Next, monks purify the grid to prepare it for the constructing of the deities before sand is finally added. Tibetan Buddhists believe that anyone who looks at the mandala will receive positive energy and be blessed. Due to the Buddhist belief in impermanence, the mandala is eventually dismantled and is ritualistically released into the world. [7]
One of the cornerstones of Chinese folk religion is the relationship between man and nature. This is epitomized in feng shui, which are architectural principles outlining the design plans of buildings in order to optimize the harmony of man and nature through the movement of Chi, or “life-generating energy.” [8] In order to maximize the flow of Chi throughout a building, its design plan must utilize specific shapes. Rectangles and squares are considered to be the best shapes to use in feng shui design. This is because other shapes may obstruct the flow of Chi from one room to the next due to what are considered to be unnatural angles. [8] Room layout is also an important element, as doors should be proportional to one another and located at appropriate positions throughout the house. Typically, doors are not situated across from one another because it may cause Chi to flow too fast from one room to the next. [8]
The Forbidden City is an example of a building that uses sacred geometry through the principles of feng shui in its design plan. It is laid out in the shape of a rectangle that measures over half a mile long and about half a mile wide. [9] Furthermore, the Forbidden City constructed its most important buildings on a central axis. The Hall of Supreme Harmony, which was the Emperor’s throne room, is located at the midpoint or “epicenter” of the central axis. This was done intentionally, as it was meant to show that when the Emperor entered this room, he would be ceremonially transformed into the center of the universe. [9]
The geometric designs in Islamic art are often built on combinations of repeated squares and circles, which may be overlapped and interlaced, as can arabesques (with which they are often combined), to form intricate and complex patterns, including a wide variety of tessellations. These may constitute the entire decoration, may form a framework for floral or calligraphic embellishments, or may retreat into the background around other motifs. The complexity and variety of patterns used evolved from simple stars and lozenges in the ninth century, through a variety of 6- to 13-point patterns by the 13th century, and finally to include also 14- and 16-point stars in the sixteenth century.
Geometric patterns occur in a variety of forms in Islamic art and architecture including kilim carpets, Persian girih and Moroccan/Algerian zellige tilework, muqarnas decorative vaulting, jali pierced stone screens, ceramics, leather, stained glass, woodwork, and metalwork.
Islamic geometric patterns are used in the Quran, Mosques and even in the calligraphies.
The Agamas are a collection of Sanskrit, [10] Tamil, and Grantha [11] scriptures chiefly constituting the methods of temple construction and creation of idols, worship means of deities, philosophical doctrines, meditative practices, attainment of sixfold desires, and four kinds of yoga. [10]
Elaborate rules are laid out in the Agamas for Shilpa (the art of sculpture) describing the quality requirements of such matters as the places where temples are to be built, the kinds of image to be installed, the materials from which they are to be made, their dimensions, proportions, air circulation, and lighting in the temple complex. The Manasara and Silpasara are works that deal with these rules. The rituals of daily worship at the temple also follow rules laid out in the Agamas.
Hindu temples, the symbolic representation of cosmic model is then projected onto Hindu temples using the Vastu Shastra principle of Sukha Darshan, which states that smaller parts of the temple should be self-similar and a replica of the whole. The repetition of these replication parts symbolizes the natural phenomena of fractal patterns found in nature. These patterns make up the exterior of Hindu temples. Each element and detail are proportional to each other, this occurrence is also known as the sacred geometry. [12]
The construction of Medieval European cathedrals was often based on geometries intended to make the viewer see the world through mathematics, and through this understanding, gain a better understanding of the divine. [13] These churches frequently featured a Latin Cross floor-plan. [14]
At the beginning of the Renaissance in Europe, views shifted to favor simple and regular geometries. The circle in particular became a central and symbolic shape for the base of buildings, as it represented the perfection of nature and the centrality of man's place in the universe. [14] The use of the circle and other simple and symmetrical geometric shapes was solidified as a staple of Renaissance sacred architecture in Leon Battista Alberti's architectural treatise, which described the ideal church in terms of spiritual geometry. [15]
In the High Middle Ages, leading Christian philosophers explained the layout of the universe in terms of a microcosm analogy. In her book describing the divine visions she witnessed, Hildegard of Bingen explains that she saw an outstretched human figure located within a circular orb. [16] When interpreted by theologians, the human figure was Christ and mankind showing the Earthly realm and the circumference of the circle was a representation of the universe. Some images also show above the universe a depiction of God. [16] This is thought to later have inspired Da Vinci’s Vitruvian Man.
Dante uses circles to make up the nine layers of hell categorized in his book, TheDivine Comedy. “Celestial spheres” are also utilized to make up the nine layers of Paradise. [17] He further creates a cosmic order of circular forms that stretches from Jerusalem in the Earthly realm up to God in Heaven. [17] This cosmology is believed to have been inspired by the ancient astronomer Ptolemy. [17]
Stephen Skinner criticizes the tendency of some writers to place a geometric diagram over virtually any image of a natural object or human created structure, find some lines intersecting the image and declare it based on sacred geometry. If the geometric diagram does not intersect major physical points in the image, the result is what Skinner calls "unanchored geometry". [18]
A mandala is a geometric configuration of symbols. In various spiritual traditions, mandalas may be employed for focusing attention of practitioners and adepts, as a spiritual guidance tool, for establishing a sacred space and as an aid to meditation and trance induction. In the Eastern religions of Hinduism, Buddhism, Jainism and Shinto it is used as a map representing deities, or especially in the case of Shinto, paradises, kami or actual shrines.
Mount Meru, also known as Sumeru, Sineru, or Mahāmeru, is the sacred five-peaked mountain of Hindu, Jain, and Buddhist cosmology and is considered to be the centre of all the physical, metaphysical, and spiritual universes. The mountain is also mentioned in some scriptures of non-Indian based religions such as Taoism, which was influenced by the arrival of Buddhism in China. There is no clear identification of Mount Meru with a particular geophysical location but it is always located in the Himalayan or Aravalli ranges.
Geomancy translates literally to "earth divination," and the term was originally used to mean methods of divination that interpret geographic features, markings on the ground, or the patterns formed by soil, rocks, or sand. Its definition has expanded over time, to include any spiritual, metaphysical, or pseudoscientific practice that is related to the Earth. In recent times the term has been applied to a wide range of other occult and fringe activities, including Earth mysteries and the introduction of ley lines and Bau-Biologie.
Religious art is a visual representation of religious ideologies and their relationship with humans. Sacred art directly relates to religious art in the sense that its purpose is for worship and religious practices. According to one set of definitions, artworks that are inspired by religion but are not considered traditionally sacred remain under the umbrella term of religious art, but not sacred art.
Mathematics and architecture are related, since, as with other arts, architects use mathematics for several reasons. Apart from the mathematics needed when engineering buildings, architects use geometry: to define the spatial form of a building; from the Pythagoreans of the sixth century BC onwards, to create forms considered harmonious, and thus to lay out buildings and their surroundings according to mathematical, aesthetic and sometimes religious principles; to decorate buildings with mathematical objects such as tessellations; and to meet environmental goals, such as to minimise wind speeds around the bases of tall buildings.
The Khajuraho Group of Monuments are a group of Hindu and Jain temples in Chhatarpur district, Madhya Pradesh, India. They are about 175 kilometres (109 mi) southeast of Jhansi, 10 kilometres (6.2 mi) from Khajwa, 9 kilometres (5.6 mi) from Rajnagar, and 49 kilometres (30 mi) from district headquarter Chhatarpur. The temples are famous for their Nagara-style architectural symbolism and a few erotic sculptures.
Originating in ancient India, Vastu Shastra is a traditional Hindu system of architecture based on ancient texts that describe principles of design, layout, measurements, ground preparation, space arrangement, and spatial geometry. The designs aim to integrate architecture with nature, the relative functions of various parts of the structure, and ancient beliefs utilising geometric patterns (yantra), symmetry, and directional alignments.
Hindu temple architecture as the main form of Hindu architecture has many different styles, though the basic nature of the Hindu temple remains the same, with the essential feature an inner sanctum, the garbha griha or womb-chamber, where the primary Murti or the image of a deity is housed in a simple bare cell. For rituals and prayers, this chamber frequently has an open space that can be moved in a clockwise direction. There are frequently additional buildings and structures in the vicinity of this chamber, with the largest ones covering several acres. On the exterior, the garbhagriha is crowned by a tower-like shikhara, also called the vimana in the south. The shrine building often includes an circumambulatory passage for parikrama, a mandapa congregation hall, and sometimes an antarala antechamber and porch between garbhagriha and mandapa. In addition to other small temples in the compound, there may be additional mandapas or buildings that are either connected or separate from the larger temples.
A thangka is a Tibetan Buddhist painting on cotton, silk appliqué, usually depicting a Buddhist deity, scene, or mandala. Thangkas are traditionally kept unframed and rolled up when not on display, mounted on a textile backing somewhat in the style of Chinese scroll paintings, with a further silk cover on the front. So treated, thangkas can last a long time, but because of their delicate nature, they have to be kept in dry places where moisture will not affect the quality of the silk. Most thangkas are relatively small, comparable in size to a Western half-length portrait, but some are extremely large, several metres in each dimension; these were designed to be displayed, typically for very brief periods on a monastery wall, as part of religious festivals. Most thangkas were intended for personal meditation or instruction of monastic students. They often have elaborate compositions including many very small figures. A central deity is often surrounded by other identified figures in a symmetrical composition. Narrative scenes are less common, but do appear.
A Hindu temple, also known as Mandir, Devasthanam, Pura, or Koil, is a sacred place where Hindus worship and show their devotion to deities through worship, sacrifice, and prayers. It is considered the house of the god to whom it is dedicated. Hindu temple architecture, which makes extensive use of squares and circles, has its roots in Vedic traditions, which also influence the temples' construction and symbolism. Through astronomical numbers and particular alignments connected to the temple's location and the relationship between the deity and the worshipper, the temple's design also illustrates the idea of recursion and the equivalency of the macrocosm and the microcosm. A temple incorporates all elements of the Hindu cosmos—presenting the good, the evil and the human, as well as the elements of the Hindu sense of cyclic time and the essence of life—symbolically presenting dharma, artha, kama, moksha, and karma.
A cosmogram depicts a cosmology in a flat geometric form. They are used for various purposes: meditational, inspirational and to depict structure – real or imagined – of the earth or universe.
Sacral architecture is a religious architectural practice concerned with the design and construction of places of worship or sacred or intentional space, such as churches, mosques, stupas, synagogues, and temples. Many cultures devoted considerable resources to their sacred architecture and places of worship. Religious and sacred spaces are amongst the most impressive and permanent monolithic buildings created by humanity. Conversely, sacred architecture as a locale for meta-intimacy may also be non-monolithic, ephemeral and intensely private, personal and non-public.
Yantra is a geometrical diagram, mainly from the Tantric traditions of the Indian religions. Yantras are used for the worship of deities in temples or at home; as an aid in meditation; and for the benefits believed given by their occult powers based on Hindu astrology and tantric texts. They are also used for adornment of temple floors, due mainly to their aesthetic and symmetric qualities. Specific yantras are traditionally associated with specific deities and/or certain types of energies used for accomplishment of certain tasks or vows that may be either materialistic or spiritual in nature. They become a prime tool in certain sadhanas performed by the sadhaka, the spiritual seeker. Yantras hold great importance in Hinduism, Jainism, and Buddhism.
Alden Taylor (Tad) Mann, is an American astrologer, writer, designer and artist who is known for his books and paintings on astrology and sacred architecture, human sexuality and gardens.
Keith Barry Critchlow was a British artist, lecturer, author, sacred geometer, professor of architecture, and a co-founder of the Temenos Academy in the UK.
Islamic ornament is the use of decorative forms and patterns in Islamic art and Islamic architecture. Its elements can be broadly divided into the arabesque, using curving plant-based elements, geometric patterns with straight lines or regular curves, and calligraphy, consisting of religious texts with stylized appearance, used both decoratively and to convey meaning. All three often involve elaborate interlacing in various mediums.
Islamic geometric patterns are one of the major forms of Islamic ornament, which tends to avoid using figurative images, as it is forbidden to create a representation of an important Islamic figure according to many holy scriptures.
Robert Edward Williams is an American designer, mathematician, and architect. He is noted for books on the geometry of natural structure, the discovery of a new space-filling polyhedron, the development of theoretical principles of Catenatic Geometry, and the invention of the Ars-Vivant Wild-life Protector System for repopulating the Western Mojave Desert in California, USA with desert tortoises.
Dillon Forte is an American tattoo artist and entrepreneur, based in Oakland and Venice, Los Angeles. Known for his use of sacred geometry-inspired patterns, Forte has been featured in Paramount Network's The Art of Ink (2018) and the Amazon Studios comedy Jean-Claude Van Johnson (2017).
Tibetan Monasteries are known for their rich culture and traditions, which are rooted in the teachings of Buddhism. An important aspect of Tibetan Buddhist monasteries is the presence of ritualistic places that are dedicated to deities. Vajrayana Buddhism contains intricate iconography that deals with deities and religious practices. To a devotee, it may appear as images and icons to bring luck or drive away evil spirits. Thangkas at monasteries show Buddha, Gurus, Yantras, andMandalas, which bring good luck, health, prosperity, wisdom, longevity, and peace.