To make a square of half the area of another, join the mid-points of its sides: the rotated square so drawn has exactly half the area. Repeat to halve again.
side of inscribed square = s ⁄ √2 · area = ½ s²
The church beside the square, not in it
Give the church a block of its own next to the market square, near a corner of it, so that the market keeps its open ground and the church its churchyard.
In the bastides the square belonged to commerce and the consuls; the church stood aside on an adjoining block, usually close to one corner of the square so that its tower closed the view down a street. Southern bastide churches are typically a single wide vaulted nave with chapels between the buttresses and a polygonal apse, often with a massive tower that could serve as a refuge.
Related rules
End the choir in a semicircle of piers; wrap an aisle (the ambulatory) around it, and open a ring of chapels off the ambulatory, each with its own altar and windows, so that the east end steps down in tiers of roofs and buttresses.
Put the hall at the heart of the house and enter it at one end, by a passage running through the house from front door to back door, screened from the hall. Open the buttery, the pantry and, between them, the way to the kitchen off that passage, at the hall’s lower end; put the family’s parlour, and the great chamber over it, beyond the hall’s upper end, where the high table stands.
Build the monastery, if possible, so that everything it needs (water, a mill, a garden and the various crafts) is inside the enclosure, so that the monks need not wander outside, which does their souls no good; and set a wise old monk at the gate, with a cell beside it.
Let all the monks sleep in one place if their number allows, each in his own bed, clothed and ready to rise, with a light burning until morning; place the dormitory where they can go straight to the church for the night office.
Receive every guest as Christ, the poor and pilgrims with the greatest care; give the abbot and the guests a kitchen of their own, so that guests arriving at unexpected hours do not disturb the brothers; lodge them in a guest house apart, in the care of a God-fearing brother.
Cite this page Chris Paton, “The church beside the square, not in it”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/bastide-church. Text, drawings and models licensed under CC BY-NC 4.0.