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The circle of wholeness and of time; perpetuity; endless duration; asceticism.  In religions:

Buddhist: The 108 beads represent the 108 Brahmins present at the birth of Buddha; the circle is the Wheel of the Law, also the Round of Existence with the individual beads of manifestation strung upon it.

Christian: The mystic rose garden of the Virgin Mary; the 165 beads are divided into five decades; each set of five decades has its own “mysteries” of the joys, sorrows and glories of the Virgin Mary.  The large beads represent the Our Father, and a Gloria, the small beads the Hail Mary.  Attribute of St. Dominic.

Hindu: The thread is the non-manifest, the beads are the multiplicity of the manifestation and the circle is Time.  The rosary is an attribute of Brahma, Siva and Ganesha.  The rosary of Siva has 32 or 64 berries of the “Rudraksha tree, and usually accompanies the figure of the “Shaivite” saint.  Other rosaries have 108 beads of Tulasi wood.

Islamic: The 99 beads are the “circular” number and correspond to the Divine Names; the 100th bead, which is the name of the Essence, can be found only in Paradise.
SYMBOLS - ROSARY
A universal symbol; wholeness, the self-contained, eternity, celestial unity; God. “God is a circle whose center is everywhere and circumference is nowhere.”
          — Hermes Trismegistus

American Indian:  The circle radiating outward and inward, as the Feathered Sun, is a symbol of the universe.  Camp circles and the circular teepee are a pattern of the cosmos with the North side as the heavens and the South side as the earth.

     The four directions of space in the celestial circle are the totality comprising the Great Spirit.  The North American Indian lodge, cross inscribed in the circle, symbolizes sacred space and is a Cosmic Center.

Buddhist:  The circle is the Round of Existence enclosing all in the phenomenal world.  Three circles in triangular form are the Three Jewels.  In Zen the empty circle is enlightenment.

Chinese:  The circle is the heavens, with the square as the earth  in the old coin; the circle with the square at the center depicts the union of heaven and earth, yin and yang. By analogy, the perfect man.  The circle is also the moving heavens which revolve around the unmoving square of the earth.

Christian:  The Church Universal; three concentric or interlocking circles depict the Trinity.  Two concentric circles signify intellect and will, according to Dante.  Twin circles, as love and knowledge, represent Christ, also his dual nature.  A Christian church frequently forms a cross inside the circle of the churchyard.
SYMBOLS - CIRCLES
Egyptian:  The winged circle is the rising sun, Ra, and the resurrection.

Greek:  The circle of Ouroboros round the Cosmic Egg was called Cronos and was defined by Pythagoras as the psyche of the universe.  Cronos was mated to Necessity, also circling the universe, hence Time and Fate were both circles.

Hindu: The circle is the Round of Existence in the phenomenal world.  The flaming circle is a symbol of Prakriti, “that which evolves, produces, brings forth.”

Islamic:  The circle is the dome; the vault of heaven; divine light.

Semitic:  The winged circle is an anionic symbol of solar gods; divinity; solar power.

Taoist:  A circle with a point in the center represents the supreme power, the Tao; the circle is also the Precious Pearl.