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Topic: Need help on this interesting fact
Replies: 3   Last Post: Mar 14, 2005 10:50 PM

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Kevin Karplus

Posts: 126
Registered: 12/6/04
Re: Need help on this interesting fact
Posted: Oct 21, 2003 4:54 PM
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In article <>, 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
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
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