Baudhāyana's bricks

Explore Baudhāyana's bricks, one of the oldest uses of fractions in geometry.

Some of the oldest uses of fractions are in the Śhulbasūtra, humanity's oldest geometry texts. This one is from Baudhāyana's Śhulbasūtra, written around 800 BCE.

*Cover an area of 7 1/2 square units with square bricks of side 1/5 unit. How many bricks are needed?*

One brick: 1/5 × 1/5 = 1/25 square unit.
Total area: 7 1/2 = 15/2 square units.
Link them: number of bricks × 1/25 = 15/2. A missing factor, so divide: 15/2 ÷ 1/25.
Divide by multiplying by the reciprocal (25): 15/2 × 25 = 375/2, that is 187 1/2 bricks.

Everything from this chapter came together: multiplying fractions, changing a mixed fraction, spotting a division, and using a reciprocal. And the answer is much bigger than 15/2, as it must be when dividing by a number less than 1: the bricks are small, so you need many.

A challenge: four fountains fill a tank in 1 day, 1/2 day, 1/4 day and 1/5 day. In one day they would fill it 1 + 2 + 4 + 5 = 12 times. So together they fill it once in 1/12 of a day. How many hours is that?

Number of pieces = total area ÷ area of one piece, which is why a small brick gives a large count.

Baudhāyana's bricks, about 800 BCE.

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