How Did Anyone Do Math in Roman Numerals?
Hacker News Comments: ▻https://news.ycombinator.com/item?id=14818633
Source: ▻http://www.washingtoncitypaper.com/columns/straight-dope/article/20854121/how-did-anyone-do-math-in-roman-numerals
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And basic Roman arithmetic is largely rather simple, even for those of us spoiled by Arabic notation. Addition is no sweat, because complex Roman numbers already use what math pros call additive notation, with numerals set beside one another to create a larger number. VI is just V plus I, after all. To add large numbers, simply pile all the letters together, arrange them in descending order, and there’s your sum. CLXVI plus CLXVI? CCLLXXVVII, or CCCXXXII. And one of the advantages of the Roman system is that you don’t need to memorize multiplication tables. What’s VI times VI? Six Vs and six Is, which converts to three Xs, a V, and an I: XXXVI.
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You’ll notice I haven’t mentioned long division—that’s where positional value really pays off. What’s CCXVII divided by CLI? The pile-and-sort method isn’t going to work here. For this one, as well as for the multiplication of larger numbers, you need an abacus. Not too much physical evidence survives, but judging from references in poems by Catullus, Juvenal, and others, and from contemporary devices found in Greece, the standard Roman abacus used glass, ivory, or bronze counters placed on a board marked off into rows and columns. (The counters were at first made of stone and called calculi or “pebbles,” the obvious root of several math-related words in English.) A later, more portable version (and this one we’ve found examples of) consisted of a metal plate with beads that slid back and forth in slots.
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