1. Triquetra is a word derived from the Latin tri- ("three") and quetrus ("cornered"). Its original meaning was simply "triangle" and it has been used to refer to various three-cornered shapes. Nowadays, it has come to refer exclusively to a certain more complicated shape formed of three vesicae piscis, sometimes with an added circle in or around it.
2. The Triquetra symbol right is actually composed of three Vesica Piscii, the holy symbol of the Pythagorean Christos. It is composed of three ‘almond-shaped’ icthyi, each with a height to width ratio of 1.73205, which is the square root of three. This ratio gave rise to the Divine number 153 (the complete mathematical ratio being 265:153, the ratio of whole numbers under 1000, which approximated the square root of 3.) 153 is the number of fish Jesus caught in the Gospel of John 21:11. When one considers that there are three Vesica Piscii in the Triquetra, the following calculation has surprising results:153 x 3 = 4594 + 5 + 9 = 181 + 8 = 9
3. The Vesica piscis has been the subject of mystical speculation at several periods of history, perhaps first among the Pythagoreans, who considered it a holy figure. The mathematical ratio of its width (measured to the endpoints of the "body", not including the "tail") to its height was reportedly believed by them to be 265:153. This ratio, equal to 1.73203, was thought of as a holy number, called the measure of the fish. The geometric ratio of these dimensions is actually the square root of 3, or 1.73205... (since if you draw straight lines connecting the centers of the two circles with each other, and with the two points where the circles intersect, then you get two equilateral triangles joined along an edge). The fraction 265:153 is a ratio of whole numbers under 1000 which approximates the square root of 3 (though 362:209 and 989:571 are actually closer approximations). The number 153 appears in the Gospel of John as the exact number of fish Jesus caused to be caught in a miraculous catch of fish, which is thought by some to be a coded reference to Pythagorean beliefs.
4. Ichthys was the offspring son of the ancient sea goddess Atargatis, and was known in various mythic systems as Tirgata, Aphrodite, Pelagia or Delphine. The word also meant "womb" and "dolphin" in some tongues, and representations of this appeared in the depiction of mermaids. The fish is also a central element in other stories, including the Goddess of Ephesus (who has a fish amulet covering her genital region), as well as the tale of the fish that swallowed the penis of Osiris, and was also considered a symbol of the vulva of Isis.Along with being a generative and reproductive spirit in mythology, the fish also has been identified in certain cultures with reincarnation and the life force. Sir James George Frazer noted in his work, "Adonis, Attis, Osiris: Studies in the History of Oriental Religion" (Part Four of his larger work, "The Golden Bough") that among one group in India, the fish was believed to house a deceased soul, and that as part of a fertility ritual specific fish is eaten in the belief that it will be reincarnated in a newborn child.Possibly before Christianity, the fish symbol was known as "the Great Mother," a pointed oval sign, the "vesica piscis" or Vessel of the Fish. Also, in ancient Greek, "fish" and "womb" were denoted by the same word ("delphos"). Its link to fertility, birth, feminine sexuality and the natural force of women was acknowledged also by the Celts, as well as pagan cultures throughout northern Europe. Eleanor Gaddon traces a "Cult of the Fish Mother" as far back as the hunting and fishing people of the Danube River Basin in the sixth millennium B.C.E. Over fifty shrines have been found throughout the region which depict a fishlike deity, a female creature who "incorporates aspects of an egg, a fish and a woman which could have been a primeval creator or a mythical ancestress..." The "Great Goddess" was portrayed elsewhere with pendulous breasts, accentuated buttocks and a conspicuous vaginal orifice, the upright "vesica piscis" which Christians later adopted and rotated 90-degrees to serve as their symbol.There are several hypotheses as to why the fish was chosen. The most probable is that it is a reference to the scripture in which Jesus miraculuously feeds 5000 people with fish and bread (Matthew 14:15-21, Luke 9:12-17, and John 6:4-13). The ichthys also may relate to Jesus as a "fisher of men," or an acronym of the Greek letters ICTYS (Iota Chi Theta Ypsilon Sigma) to the statement of Christian faith "Iesous Christos Theou Hyios Soter: Jesus Christ, Son of God, Savior".Though there is no direct evidence, the ichthys may simply be an adaptation of the mystic/mathematical symbol known as the Vesica Piscis. The length-height ratio of the vesica piscis, as expressed by the mystic and mathematician Pythagoras, is 153:265, a mystical number known as "the measure of the fish." In the biblical story in which Jesus aids his disciples to catch fish, Jesus catches exactly 153 fish.The name ichthys was also associated with Adonis, the central character in one of the 1st-century mystery religions (specifically, the version used in Syria). Like many other mystery religions, the religion of Adonis adopted certain mystic aspects of Greek philosophy, which may have included the Vesica Piscis of Pythagoras. In astrology, an astrological age is determined by the constellation in which the Sun appears during the vernal equinox. Since each sign on the zodiac belt shifts an average of one degree in 70 years, while 360/12 = 30, each astrological age lasts 70 x 30 = 2,100 years. The astrological age of Pisces coincided with the birth of Jesus Christ — approximately 2,000 years ago. Babylonian mythology tells of two fishes that pushed ashore a giant egg, from which emerged the fertility corn-goddess Atargatis and her lover-son Ichthys, who dies and is reborn annually. The myth of Ichthys and the sign Pisces later became connected with Christianity. Directly across the zodiac from Pisces lies the sign of Virgo, symbolizing the virgin grain goddess of ancient Greece and also connected with the Virgin Mary of Christian mythology, whose birthday is liturgically celebrated on September 8, when the sun crosses the midpoint of the sign Virgo.
5. The fish symbol was often drawn by overlapping two very thin crescent moons. One represented the crescent shortly before the new moon; the other shortly after, when the moon is just visible. The Moon is the heavenly body that has long been associated with the Goddess, just as the sun is a symbol of the God. The link between the Goddess and fish was found in various areas of the ancient world: for instance, in China, Great Mother Kwan-yin often portrayed in the shape of a fish; in India, the Goddess Kali was called the "fish-eyed one"; in Egypt, Isis was called the Great Fish of the Abyss; in Greece the Greek word "delphos" meant both fish and womb (the word is derived from the location of the ancient Oracle at Delphi who worshipped the original fish goddess, Themis. The later fish Goddess, Aphrodite Salacia, was worshipped by her followers on her sacred day, Friday. They ate fish and engaging in orgies. In later centuries, the Christian church adsorbed this tradition by requiring the faithful to eat fish on Friday.) In ancient Rome Friday is called "dies veneris", or Day of Venus, the Pagan Goddess of Love; in Scandinavia, the Great Goddess was named Freya; fish were eaten in her honour; in the Middle East, the Great Goddess of Ephesus was portrayed as a woman with a fish amulet over her genitals.
6. In the recitation of the Rosary, corresponding to the recitation of three beads, the prayer of the Ave Maria is repeated 153 times."There is way to much on the number 153 to sumarize here but a little searching can tell you more if you are interested. 153 is also used in the construction of the Great Pyramid (pyre - amid, being fire within).
I think it is safe to say the three fish is a uniquely feminine form of the trinity. Related as it is to the dying and resurecting Gods, and their mothers or lovers, we see also the implication of both reincarnation and spiritual rebirth, the immortality of spirit, and spiritual evolution. When it also includes a circle we have a slightly different meaning in that the circle represents the void from which the three are springing into life. The three that come from the one are God the daughter(our personal God), God the traveler into time and space(us), and the soulmate... perhaps.