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Roman multiplication

Actually, multiplication is a kind of accelerated addition.

 


Explanation

First, an example using Arabic numerals. Take 21 × 39 = 819. You can always double the number 39, then you will get 78, 156, 312, 624, 1248, and so on. The number 21 can be built from powers of 2, so from 20 = 1 ,   21 = 2 ,  22 = 4 ,  23 = 8 ,  24 = 16, where 21  = 16 + 4 + 1. Now add up the valid rows.

21 ×         39
 
1 39
  2 78
4 156
  8 312
16 624
  ¯¯¯¯¯¯
  Total 819

So you add up 39 + 156 + 624 = 819. The same also with Roman numerals.

    ⅩⅩⅠ        × ⅩⅩⅩⅨ
       
  ⅩⅩⅩⅨ
    ⅠⅠ ⅬⅩⅩⅧ
  ⅭⅬⅥ
    ⅭⅭⅭⅩⅠⅠ
  ⅩⅥ ⅮⅭⅩⅩⅣ
      ¯¯¯¯¯¯¯¯¯¯¯¯¯¯
  Total    ⅮⅭⅭⅭⅩⅨ

You can just add everything together, because ⅩⅩⅩⅨ + ⅭⅬⅥ + ⅮⅭⅩⅩⅣ = ⅮⅭⅭⅭⅨ. And so the Romans could perform a multiplication using only addition.

The Romans were not stupid.

 


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