This is interesting for those developing algorithms –
The Romans had a clumsy way of writing numbers that made multiplication next to impossible to carry out. Just try to verify the result of the multiplication
XIX × XXVII = DXIII
and see for yourself what the problem is. But human ingenuity came to rescue and they invented a method whereby multiplication could be reduced to addition, doubling and halving — something that the Romans could cope with.
This method was forgotten and re-invented later; it is also known as the “Russian Method”.
Other cool math ideas from Professor Fekete are available here.
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My introduction to professor Fekete was through his thought-provoking articles on gold, gold standard and Austrian economics. They are highly recommended, and I would suggest you to start from 2002 and go toward later years.
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Speaking of multiplication, here is how the Mayan’s did it (h/t: Inti Pedroso @intipedroso)
even though this guy claims the method came from Vedic India.