Re "The Trinity is a theological formulation in Christianity ... not a philosophical idea. :
Yes, but the Christian theologians were indebted to the Neoplatonists, especially the divine Plotinus and Iamblichus. The One is at the top of the hierarchy. The first emanation is Nous (Divine Mind). From Nous proceeds the World Soul. There are similar notions in Kabbalah (which also pinched its ideas from Greek Platonists) with their Supernal Triad - the three heavenly Sefirot (Kether, Chokmah and Binah). Those ideas have their origin in number "theory". In Christian terminology you could say that the original "creation" occurs when the primal One (the Father) withdraws to leave space for the other (the Son). A split is avoided because the Father has knowledge of and loves the Son. The love is the Holy Spirit. Bleeding obvious when you think about it.