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The action of repeated [[addition]]s: $a\times b=\underbrace{a+a+\cdots+a}_{\hbox{$b$ times}}$. | The action of repeated [[addition]]s: $a\times b=\underbrace{a+a+\cdots+a}_{\hbox{$b$ times}}$. | ||
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| + | By looking at it from a geometric point of view, it is not difficult—although not trivial either—to see that $a\times b=b\times a$. | ||
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| + | An interesting problem regards the complexity, or cost of multiplication. In 1960, Karatsuba improved on the "school method". | ||
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| + | == Links == | ||
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| + | * [http://www.ccas.ru/personal/karatsuba/divcen.pdf Karatsuba recollections and comments on his methods]. | ||
The action of repeated additions: $a\times b=\underbrace{a+a+\cdots+a}_{\hbox{$b$ times}}$.
By looking at it from a geometric point of view, it is not difficult—although not trivial either—to see that $a\times b=b\times a$.
An interesting problem regards the complexity, or cost of multiplication. In 1960, Karatsuba improved on the "school method".