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Re: Need help on this interesting fact
Posted:
Oct 21, 2003 4:54 PM


In article <sgvapvckrjts28upircgte0te8n5k72jv5@4ax.com>, 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 karplus@soe.ucsc.edu http://www.soe.ucsc.edu/~karplus life member (LAB, Adventure Cycling, American Youth Hostels) Effective Cycling Instructor #218ck (lapsed) Professor of Computer Engineering, University of California, Santa Cruz Undergraduate and Graduate Director, Bioinformatics Affiliations for identification only.
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