Euler Identity in Home

[Manolo Sobrino]

There was a long version of this post with accuracy/precision tests, fun and excitement, but it's definitely overkill and you should always check this kind of claims anyway... Short version:

a) You can't justify using more significant digits for the answer than those of the argument. That's not how things work in the real world of measuring things. The answer you get from the Prime is really zero, as the consistent way of writing it is 0E-12.

b) The TI calculators perform consistently with it's 14 digit claimed accuracy. They get zero because that's the correct 14 significant digit result for their stored value of Pi. I can't find strange jumps in the neighbourhood of Pi. Actually they give you the meaningful answers. No tricks, no special values, go figure.

c) Digital garbage just gives you a lot of information about precision.

d) The Prime results likely correspond to calculations with at least 25-digit precision of the 12 digit rounded value of Pi.

e) They could make Colin happier by using a value of Pi with more digits, as probably this can be done he has a point. They should be rounded in a sensible way for the final accurate answer anyway.

f) Due to rounding numbers to 12 digits after every operation (this took a while) and then performing those at least 25-digit precision calculations, the TI results for SIN have actually more significant accurate digits in the neighbourhood of Pi.