The number three is the only number that is the sum of its parts: 1+2=3. Therefore it is the only true "unity" apart from One, and it is partly for this reason that many religious entities are triune in nature.
In Christianity The Father, Son and Holy Ghost form a Trinity much like that of the ancient Egyptian hierarchy of Pharaoh, Falcon and Sun (Below, Between and Above). The fact that the Holy Spirit is symbolized by a dove emphasizes this similarity of Man, the intermediary bird, and God. (Birds are symbolic of communication with the divine; it is said that their songs whisper the secrets of heaven.) It is also a common theme to find a 'Holy Family,' as with Osiris, Isis and Horus, for instance, or Joseph, Mary and Jesus.
It was three wise men who brought the gifts of gold, frankincense and myrrh to the newborn Messiah. Acharya S. and others maintain that the extra-biblical tradition of "three" wise men is based on the three gifts, and also the three stars of Orion's belt - which is in close proximity to Virgo, which many maintain is the "star in the east." (See: Virgo; Virgin Mary; Venus; Aphrodite; Solar Christ; they will be updated/created very soon.)
In Hinduism the year and day are divided in three, personified as Brahma the Creator (dawn and spring), Vishnu the Preserver (noon and summer), and Shiva the Destroyer (night and autumn-winter).
For this same reason it is symbolic of the reconciliation of opposites, as with Hegel's dialectic: "thesis + antithesis = synthesis." The holy family is triune because male and female, light and dark, are reconciled in the product of their union. Adam and Eve had three children: Abel, or meekness, and Cain, whose severity devoured Abel; in the latter's stead was placed Seth, the reconciliatory principle of equilibrium, the Middle Path. (See: S.L. MacGregor Mathers's Kabbalah Unveiled)
It is both a lunar and a solar number. The moon has three major phases - the two crescents and the full moon, while the sun has three primary points in its existence: the low winter solstice, or Christmas; the high summer solstice, or Baptism; and the two equinoxes of March and September (the Fall and Redemption of Man), when day and night are equal. (Therefore: the longest night, the longest day, and the two points of equilibrium.)
It is commonly found in folklore, as in three wishes, three tries, three princes or princesses, and three witches. Three is the second triangle number (1 being the first), therefore its symbol is naturally this figure.
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