I've recently started reading this:
https://books.google.com/books/about/The_Crest_of_the_Peacock.html?id=ymud91nTc9YC#v=onepage&q&f=false
and learned some lovely things about multiplication in ancient Egypt. They did theirs by producing a table of doubles of one multiplicand, then representing the other in binary. The entries in the table of doubles corresponding to binary ones were then summed!
@Dyoung Also known as "Russian Peasant Multiplication", it can be generalised to powers (and is used in multi-precision packages) and to multiply and take powers of matrices.
It's really cool!
@Dyoung It's a really cool algorithm. A variation of it is used in cryptography, too, involving squaring instead of doubling:
https://robjlow.blogspot.com/2017/11/russian-peasant-cryptography.html
@RobJLow Absolutely!
(Though I think I said this already over here: https://mathstodon.xyz/@ColinTheMathmo/109842078590341971 )
Did you read this?
http://www.solipsys.co.uk/new/RussianPeasantMultiplication.html?wb12mn
@ColinTheMathmo @Dyoung I'm sure I have: I was, I'm afraid, doing my usual "eagerly reply to the first post without looking at the replies already there" thing. 😳