Śaṅku





A Śaṅku, or gnomon, is an object whose shadow is measured and used in astronomical calculations. Many of the early Indian astronomers used gnomons in calculating quantities such as the time of day, the cardinal directions, the lagna, declination, right ascenscional difference, etc.

Often it was in the form of a vertical pole. Lalla (who lists the śaṅku as one of the 12 instruments of astronomy ) describes the construction of one in. He says it must be made with a compass to ensure uniform width, be made of excellent timber, 6 aṅgulas around and 12 aṅgulas high, set on a board levelled by water, and straightened with 4 plumbs. Nīlakaṇṭha describes a similar construction, but his śaṅku tapers at the top to a point, "like a rose bud".

In a large Samrāṭ-yantra, the staircase structure itself is the śaṅku, casting a shadow line across the two large, stone arcs on either side of it. The edge of the shadow-casting wall is referred to by Bapudeva as a śaṅkupāli.

In calculation, the gnomon's shadow can be considered the bottom of a right triangle. The imaginary line between the top of the gnomon and the end of the gnomon's shadow can be considered a hypotenuse (chāyā-karna ). Thus the trigonometric functions of the early Indian astronomers, such as jyā and koti-kyā (which would eventually become the modern sine and cosine functions), can be used to perform calculations on the heavens. For example, Bhāskara II gives a method of calculating the circumference of the Earth at one's current latitude, using trigonometry of the gnomon shadow.