How did the Romans calculate?
cacm.acm.org
cacm.acm.org
Isn't that the etymology of calculate? To reckon with pebbles on a counting-board?
This behaviour shouldn't be surprising to us: after all, we ourselves let our calculations be done in binary, and only use decimal numerals to record the results.
Makes sense because it's quite impossible to use those numerals directly. Fibonacci and the modern decimal numeral system came much, much later.
The emphasis is on "I believe". I would expect some documents which attest that but maybe no such luck. Like "posca", maybe it was considered too common sense to be worth written down.
On the other hand what amazes me is the thought that the entire WW2 was fought flying planes that were designed and built without the slightest trace of electronic calculator coming in aid. There's integrals and derivatives and transcendental functions, how the heck did they manage to do that with pen and paper?
I know they had tables of logarithms and trigonometric functions and some mechanical calculators but come on.
> The slot marked with a circle ○ is used for the ounces. Since 1 as (pound) has 12 ounces, this slot contains five single beads at the bottom and a six beads at the top. Thus 5+6=11 ounces can be represented.
For those puzzled by the language, it's simple once you get past it:
* Except the two rightmost columns, all columns are decimal scale, in increasing powers of 10 from right to left (I = 10^0, X = 10^1, C = 10^2, etc.). For each power of 10, each of the 4 beads in each bottom slot represents 1, each of the single beads in each top slot represents 5. Thus each column represents from 0 to ([4 bottom beads x 1] + [1 top bead x 5] =) 9. Multiply that by the slot's power of 10.
* The column labled O, second from right, represents ounces and is duodecimal because there are 12 ounces in a pound. Each of the 5 beads in the bottom slot represents 1; the lone bead in the top slot represents 6. Thus the column can represent 0 to (6+5=) 11 ounces.
* They don't know how the right-most slot was used; maybe it was for fractions of an ounce.
That's crazy considering how ubiquitous the Romans were.
It originated with the ancient Sumerians ..., was passed down to the ancient Babylonians, and is still used—in a modified form—for measuring time, angles, and geographic coordinates.
The number 60, a superior highly composite number, has twelve factors, namely 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60, of which 2, 3, and 5 are prime numbers. With so many factors, many fractions involving sexagesimal numbers are simplified.- 12 beard hairs in a corn - 5 corns in an inch - 12 inches in a foot - 5 feet in a spinner - 12 spinners in a chain - 5 chains in a football field - 12 football fields in a click
I am glad I don't have to do modern physics and mathematics using the Roman numerals.