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 college quadrangle
Build a college as one closed court: ranges of chambers on its sides, entered by staircases from the court, each staircase serving a few sets of rooms on every floor; set the chapel, the hall with its kitchen and buttery, and the library into the ranges, and enter the whole by a single gate under a tower, where the porter keeps it.
The first colleges grew piecemeal: Merton’s Mob Quad was put together between 1288 and 1378 from buildings raised as money allowed. William of Wykeham’s New College, built at once in 1379–86, was the first planned as a whole: chapel and hall end to end on one side of a great court, the library and the chambers round the others, the warden’s lodging over the gate. It became the pattern. Magdalen (1474–80) copied it with a cloister; Wadham (1610–13) is the same plan made symmetrical; and Cambridge built its colleges the same way.
The plan suited a community that lived, ate and prayed together and had to be kept in order. The court was closed to the town, the gate shut at night; there were no corridors, only staircases rising from the court, so that every room was reached past the doors of the court and under the eyes of the college. The hall was planned like the hall of a house, with its screens passage, buttery and kitchen at one end and the high table at the other.
The type outlived the Gothic manner it was born in. When the colleges rebuilt in the classical manner, at Peckwater or Queen’s, they kept the court and the staircases and changed only the dress; New College’s Garden Quadrangle (1682–1707) was the first court opened on one side to a garden.
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 college quadrangle”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/college-quadrangle. Text, drawings and models licensed under CC BY-NC 4.0.