In article <firstname.lastname@example.org>, MB wrote: > (pi^4 + pi^5)^(1/6) = e > > This piqued my curiosity. I confirmed the truism on my calculator, but I > can't seem to prove it. > > Can someone supply the proof or give me some hints?
Nope, it isn't true. It is a good approximation, but not exact.
According to my (HP) calculator, the numbers are only the same to about 8 digits. I suspect that manufacturers who use lower precision or are sloppier about carrying guard digits make calculators that can't distinguish them.
e approx 2.71828182846 (pi^4+pi^5)^(1/6) approx 2.71828180862
Using another calculation (the gnuplot program) I get e approx 2.71828182845905 (pi^4+pi^5)^(1/6) approx 2.71828180861191
Again, the calculations indicate that the numbers agree to only 8 places.
-- Kevin Karplus email@example.com http://www.soe.ucsc.edu/~karplus life member (LAB, Adventure Cycling, American Youth Hostels) Effective Cycling Instructor #218-ck (lapsed) Professor of Computer Engineering, University of California, Santa Cruz Undergraduate and Graduate Director, Bioinformatics Affiliations for identification only.