A triangle has three angles; a tricycle has three cycles or wheels, and the Trinity has three . . . nities??

Well, not exactly.

The Trinity refers to a belief about God, expressing the fact that the unity of His being exists (or subsists, to use the theological word) as three persons-Father, Son, and Spirit.  It is one of the most fruitful conceptions of Christian theology.

Autobiographies were unknown in the Greco-Roman world.  A theologian who plumbed the depths of the trinitarian nature of God and the meaning of person wrote the first autobiography.  In considering the personal nature of God, Augustine essentially developed the understanding of personhood that was the Western tradition until modern times.  His discovery of personality was new and provided one of the distinguishing marks of the Christian civilization that replaced the Greco-Roman civilization.

The Trinity has often been distorted or misunderstood by Christians, and denied by rationalists and sometimes by biblicists across the centuries.  The word “Trinity” is not found in the Bible and the doctrine was first formally expressed in the fourth century, but its content is biblical.  A triadic conception of God is visible in several places in Scripture, among them the statement of the Great Commission in Matthew 28 and the baptism of Jesus in Luke 3.

From a practical point of view, something like the Trinity is necessary to explain how God is not a supreme egotist or a schizophrenic prior to the creation.  How was His love expressed when He was all there was?  With whom did He communicate?  A multiplicity within Himself-a divine society, so to speak-explains whom He loved and how communication could occur.  A solitary, undifferentiated monad does not.

From a philosophical point of view, Christians are not stuck with the classical problem of the one and the many (or unity and diversity).  God is both one (in essence) and multiple (in person).  There is unity and diversity as far back in the Christian system of thought as it is possible to go.