Posts: 1,792
Threads: 62
Joined: Jan 2005
Hi, Massimo --
Quote:
Sorry Karl, shouldn't that be:
HP-41: sin (3.141592654 rad) = -4.1 x 10-10 vs -4.10206761537 x 10-10 ?
That also is a correct calculation, but my point was to reveal the ensuing digits of pi by calculating a truncated (not rounded) value of pi in radians mode. I've gone through the exercise several times in the Forum, but didn't save a bookmark to those posts:
sin(pi - x) = sin(pi)*cos(x) - cos(pi)*sin(x)
= 0 * cos(x) - (-1)*sin(x)
= sin(x)
x represents the truncated digits. For very small x, sin(x) ~= x, so the result produces a limited string of those digits.
The excellent mathematical routines developed for the Saturn microprocessor (debuting with the HP-71B) were ported to the Pioneer-series calculators. No other calculator I own matches the quality of the Saturn mathematics, although the TI-89 might. It also seems likely that Valentin's vintage Sharp pocket computers could meet or exceed the accuracy.
-- KS