The cord stretched along the diagonal of a rectangle produces as much area as the cords along its two sides together; use this to set out right angles and to make squares of any required area.
d² = a² + b²; e.g. cords of 3, 4, 5 or 5, 12, 13 units
Find the cardinal points with a gnomon
Set a vertical rod at the centre of the levelled site, draw a circle round it, mark where the tip of its shadow crosses the circle before and after noon, and join the two marks: that line runs east–west.
E–W = chord through the morning and afternoon shadow points; N–S ⟂ through its midpoint
The shadow of a vertical rod is symmetrical about noon, so the two points where it touches a circle centred on the rod lie on an east–west line (to within the small daily change in the sun’s declination, for which the treatises give a correction). The perpendicular through the midpoint, found by swinging cords from each mark, gives north–south. Vitruvius describes the same method for the laying out of Roman towns.
Every Hindu and Buddhist monument in this chapter was set out this way. The temple usually faces east, towards the rising sun; the stupa has gates at the four cardinal points; Angkor Wat, exceptionally, faces west.
Related rules
Imagine the vāstupuruṣa lying face down on the diagram with his head in the north-east and his feet in the south-west, held down by the gods who occupy the padas; do not place walls, pillars or doors on his vital points.
Open the railing at the four cardinal points and mark each opening with a torana: two posts carrying three curved architraves with scrolled ends, crowned with Buddhist emblems.
Break each face of the square sanctum into projections (rathas), three, five, seven or more, that step forward towards the central one, and carry them up unbroken through the wall and the tower.
tri-ratha 3 · pancha-ratha 5 · sapta-ratha 7 projections per face
Classify the temple by the shape of its crown: square is nāgara, octagonal drāviḍa, round (or apsidal) vesara.
Angkor Wat reverses the usual eastward orientation: its entrance, causeway and principal approach face west.
Cite this page Chris Paton, “Find the cardinal points with a gnomon”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/gnomon-orientation. Text, drawings and models licensed under CC BY-NC 4.0.