Sacred geometry gives special or holy meanings to certain geometric shapes and proportions. It is connected to the belief in a divine creator who is considered a 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 also applies to sacred spaces like temenoi, sacred groves, village greens, pagodas, holy wells, Mandala Gardens, and the creation of religious and spiritual art.
As worldview and cosmology
The idea that a god created the universe using a geometric plan is very old. Plutarch wrote that Plato believed this, quoting him as saying, "God geometrizes continually" (Convivialium disputationum, liber 8,2). Later, the mathematician Carl Friedrich Gauss changed this quote to "God arithmetizes."
Johannes Kepler (1571–1630) also believed that the universe has a geometric structure.
Natural forms
According to Stephen Skinner, the study of sacred geometry began with observing nature and the math rules that are active in nature. Many shapes found in nature can be connected to geometry. For example, the chambered nautilus grows in a steady way, and its shell forms a spiral shape that gets wider as it goes out. Also, honeybees build hexagon-shaped cells to store their honey. These patterns are sometimes seen as examples of sacred geometry and are considered evidence that geometric shapes play an important role in the natural world.
Representations in art and architecture
Sacred geometry was used in the designs of ancient Egyptian, Indian, Greek, and Roman buildings. Medieval European cathedrals also used symbolic shapes. In India and the Himalayas, temples and forts were built using mandala and yantra designs. Sacred gardens, called Mandala Vaatikas, were also made using these same principles.
The Vitruvian Man drawing by Leonardo da Vinci showed how the human body and ancient buildings followed sacred geometry rules. This drawing was based on the earlier writings of the Roman architect Vitruvius.
Mandalas are made of repeated geometric shapes. In Buddhism, they include circles and squares placed evenly around a center. Deities or symbols of deities are placed inside these shapes because Buddhists believe gods can appear in mandalas. Mandalas can be made with sand, paint, or other materials. Tibetan Buddhists create sand mandalas, which are then destroyed in a ritual. To make a mandala, two lines are drawn on a grid. These lines, called Brahman lines, must meet exactly at the center. The mandala is then divided into thirteen parts through trial and error. Monks clean the grid before adding sand. Tibetan Buddhists believe looking at mandalas brings good energy. Because of the belief in impermanence, mandalas are later destroyed and scattered.
A key part of Chinese folk religion is the connection between people and nature. This is shown in feng shui, which uses building designs to balance human life and nature through the movement of Chi, or "life-generating energy." Rectangles and squares are preferred in feng shui because other shapes may block Chi. Doors should be placed proportionally and not directly opposite each other to avoid Chi moving too quickly.
The Forbidden City in China uses feng shui principles in its design. It is shaped like a rectangle over half a mile long and wide. Important buildings are placed along a central axis, with the Hall of Supreme Harmony at the center. This symbolized the emperor’s role as the center of the universe.
Islamic art often uses repeated squares and circles, which are sometimes overlapped or combined with arabesques to create complex patterns. These patterns can cover entire surfaces, frame decorations, or appear in the background. Over time, patterns became more complex, from simple stars in the 9th century to 14- and 16-point stars by the 16th century. Geometric designs appear in many Islamic items, such as carpets, tiles, ceramics, and metalwork. These patterns are also found in the Quran, mosques, and calligraphy.
The Agamas are religious texts in Sanskrit, Tamil, and Grantha that describe temple construction, idol creation, worship practices, and spiritual teachings. Detailed rules in the Agamas guide temple design, including where temples should be built, the materials used, and the size and proportions of structures. The Manasara and Silpasara are texts that explain these rules. Temple rituals also follow these guidelines.
Hindu temples use the Vastu Shastra principle of Sukha Darshan, which means smaller parts of the temple should mirror the whole. This repetition reflects natural fractal patterns. Every part of the temple is proportional to others, a concept known as sacred geometry.
Medieval European cathedrals often used geometry to help people understand the divine through mathematics. Many had a Latin Cross floor plan. During the High Middle Ages, Christian thinkers described the universe as a microcosm. Hildegard of Bingen wrote about seeing a human figure inside a circle, which was later interpreted as Christ and humanity within the universe. This idea may have inspired Leonardo da Vinci’s Vitruvian Man.
In Dante’s The Divine Comedy, circles represent the nine levels of hell and the nine levels of heaven. He also used circular shapes to show a cosmic order from Earth to Heaven, inspired by the ancient astronomer Ptolemy.
At the start of the Renaissance, simple and regular shapes like circles became central in European architecture. Circles symbolized nature’s perfection and humanity’s place in the universe. Leon Battista Alberti’s writings on architecture emphasized the use of circles and symmetrical shapes in sacred buildings.
Unanchored geometry
Stephen Skinner points out a problem with some writers who place a geometric shape over almost any picture of a natural object or a human-made structure. These writers often notice some lines that cross the picture and say it is connected to sacred geometry. If the geometric shape does not cross important physical points in the image, Skinner calls this type of geometry "unanchored geometry."