Euler Identity in Home

[Joe Horn]

(04-15-2014 10:53 PM)Manolo Sobrino Wrote:  ... you can specify a value of sin(Pi) with 11 decimals ... check the example sin(pi*(1+1E-11))....

<takes deep breath to calm down> There you go again, insisting on talking about pi, when we are specifically talking about a number that is NOT PI, namely, EXACTLY 314159265359/10^11. THAT'S NOT PI, and it's NOT AN APPROXIMATION either. It's an EXACT number, the exact ratio of two integers. And exactly that many radians does in fact have an exact sine. TI can't find it. That's a Good Thing? HP does find it. That's a Bad Thing?

(04-15-2014 10:53 PM)Manolo Sobrino Wrote:  ... And the results from a TI, that in this case are decent and accurate are bad for you, because it's a TI??

No. The result given by TI for the sine of 314159265359/10^11 is neither decent nor accurate, not because it's a TI, but because it's wrong. I couldn't care less who made the calculator. Remember, I was the guy who blew the whistle on the horrible square root accuracy bug in the HP 30S (not to mention the zillion other HP bugs I've reported over the past few decades). Finding HP bugs is my #1 hobby; it actually gives me a visceral thrill when I find one. But HP gets this sine right.

(04-15-2014 10:53 PM)Manolo Sobrino Wrote:  And as they [TI] get it right you suggest that they're doing tricks???

Your insisting that TI's answer is "right" does not make it right. Just look at all the mental gymnastics you've posted in this thread, attempting to justify TI's erroneous result. But then look at the simplicity of HP's position. Does sin(exactly 314159265359/10^11 radians) have a value that's exactly defined by Maths? Yes. Is HP's result closer to it than TI's? Yes. Period.

(04-15-2014 10:53 PM)Manolo Sobrino Wrote:  Amicus Plato, sed magis amica veritas.

Oh? If truth be so precious, then why are you defending TI's false result for sin(314159265359/10^11), and denigrating HP's true result?

Remember, we're talking about the EXACT value 314159265359/10^11 here, not an approximation of pi or of anything else. Anything else in this discussion is a digression.