17 / ANTIQUITY TO THE RENAISSANCE

Bhaskara I

c. 600–680 CE·India · associated with Asmaka

Ten reeds tie into a bundle, and ten bundles into a sheaf. Where a digit sits says which one it counts, and an empty place needs a mark.

01 / DECIMAL PLACE VALUE

What does each place count?

Tie loose reeds into tens and tens into hundreds. Each tray is one place, and a place holds only 0 to 9.

An empty tray still needs a mark, or 205 looks like 25. Then read a number his way: in words from the ones up, and in figures.

Reeds:

Number:

1 bundle = 10 reeds · 1 sheaf = 10 bundles = 100 reeds · one fixed scale

THE IDEAA digit’s value depends on its place: each place to the left is worth ten times as much. A zero keeps an empty place, so 205 is not 25.

Wrote a commentary on Aryabhata in 629.
Wrote numbers in word numerals and also in figures, with a small circle for zero.
Also recorded a remarkably accurate fractional approximation to sine.

His rational approximation estimates sine using arithmetic, without reading a table.

Commentary turns terse mathematical rules into procedures a reader can follow.