Қасиетті геометрия: нысандар мен пропорциялардың символдық мағынасы

Symbolic and sacred meanings ascibed to certain geometric shapes

Sacred geometry ascribes symbolic and sacred meanings to certain geometric shapes and certain geometric proportions. 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". Johannes Kepler (1571–1630) believed in the geometric underpinnings of the cosmos. 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."

According to Stephen Skinner, the study of sacred geometry has its roots in the study of nature, and the mathematical principles at work therein. 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. This is because Buddhists believe that deities can actually manifest inside the mandala. 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. 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. 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. Tamil, and Grantha 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.

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. These churches frequently featured a Latin Cross floor plan. 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. 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. 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. He further creates a cosmic order of circular forms that stretches from Jerusalem in the Earthly realm up to God in Heaven.