Posts: 1,792

Threads: 62

Joined: Jan 2005

Hi, Massimo --

Quote:

Sorry Karl, shouldn't that be:

HP-41: sin (3.14159265**4** 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