Computing sin(0.5 radians) on an abacus - video

[mklotz]

To pick a nit, the device she is using is a soroban, the Japanese form of the abacus.

It is distinguished by having only one 'five' bead; the Chinese form has two. I suppose having two helps with borrowing when subtracting. As an example subtract seven from twelve. You start with 1 in the tens column and 2 in the ones column. Borrow by removing the one bead from the tens column and add two fives to the one column. Now subtract a five and two one beads from the the ones column and you're left with a single five bead.

I suppose with the soroban, a bit of mental work is needed. Subtracting seven is the same as subtracting ten and adding three. Therefore, remove the one bead in the tens column and mentally add three to the two in the ones column. Mentally noting that the result is five, remove the two beads there and add a five bead.

The ancient Romans used the same principles. They had a counting table with parallel grooves into which they placed small stones. (Some still survive from Pompeii.) In Latin these pebbles were known as calculi. It is from this root that we get 'calculate' and 'calculus'.