The concept of the ideal city being a perfect geometrical structure has its roots in the Pythagorean philosophy of number symbolism. For the Pythagoreans, the mystical cosmos could be understood through geometry and numerology, through perfect and pure numbers. These philosophies carried through into neo-Pythagorean, Platonic, and Neoplatonic philosophies. In John of Patmos's Book of Revelation, the image of heaven is in the form of a city. The shape of this city is heavily influenced by Neoplatonic geometry, and in the Bible God proclaimed that "You have ordered all things in measure, number and weight" (Wisdom: 11:21). Although Early Christianity was reluctant to accept pagan wisdom in the fourth century, Augustine claimed that they came close to the truth because of their observations of the pattern of creation through nature. Through the writings of Augustine, the numbers of the Pythagorean concept of the decad retained their significance in Christianity (Augustine (1972) The city of God. Penguin Books, Harmondsworth). This is illustrated where Plato is depicted as a central figure in Raphael's "School of Athens," commissioned by Pope Leo X in 1509. Plato is holding a copy of the Timaeus, a dialogue which tells the story of the origin of the cosmic system and man's place within it. The pagan tradition of numerology and geometry was revered in the highest places throughout the Renaissance and beyond. It became enmeshed into the wisdom of the macrocosm (the heavens) and how it was reflected within the microcosm (earth) through the perfection of its geometry, which became enmeshed in the symbolism of the ideal city and the ancient unsolved problem of squaring the circle.
Morrison, T. (2019)., Utopian cities, in B. Sriraman (ed.), Handbook of the mathematics of the arts and sciences, Dordrecht, Springer, pp. 1-16.
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