Euler Identity in Home

[Joe Horn]

(04-05-2014 09:54 PM)ColinJDenman Wrote:  But let us never forget that the correct answer to sin(pi) is zero. Some bits of the Prime know this. Bits that don't, shouldn't be there.

Sorry for beating a dead horse, but you are assuming that Prime's Home mode is even CAPABLE of expressing sin(exact decimal value of pi). But it isn't, because it CAN'T, because NO digital calculator ever made is capable of expressing the exact decimal value of pi. The closest that Prime's Home mode can get is exactly 3.141592653590000000000.... And the CORRECT answer for the sin of THAT is NOT zero, because as you can see, the argument is not pi, but in fact differs from pi in an infinite number of its digits.

You might be thinking, "But I pressed sin(pi), so it should calculate sin(pi)." Wrong. You pressed sin(pi rounded to n decimal places). And that's very different. There is a difference between what you are intending to do, and what you are actually doing.

You say that you like the fact that the HP-65 returns zero for sin(exactly 3.1415926540000000000... radians), and since newer HP models don't return zero, we're going backwards? Ah, but you shouldn't like the HP-65's result, because zero is the wrong answer for THAT. The CORRECT answer for THAT is -4.102067615373566...E-10. So the HP-65 should return it rounded to 10 significant digits, namely, -4.102067615E-10. But it doesn't. The newer models do. So we're not going backwards at all.