17 Dec
2003
17 Dec
'03
11:17 p.m.
At 9:47 PM 9/20/95, Ian Goldberg wrote: ....
- Ian "I heard that 'x*y=[(x+y)/2]^2 - [(x-y)/2]^2' is a patented way to multiply numbers of the same parity. Can anyone verify this and/or produce a reference?" .... That trick is probably at least 200 years old. There were once "quarter square" tables published that started i q(i) 000 000 001 000 002 001 003 002 004 004 005 006 etc. i [1^2/4]
It works for all parities. ab = q(a+b) - q(a-b) These tables were published in nautical navigation books. Mechanical analog computers sometimes used this trick to multiply shaft positions. There would be a cam that computed the square of one angle, expressed as another angle.