Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

 Messages: [ Previous | Next ]
 Kevin Karplus Posts: 126 Registered: 12/6/04
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 #218-ck (lapsed)
Professor of Computer Engineering, University of California, Santa Cruz
Affiliations for identification only.

--
submissions: post to k12.ed.math or e-mail to k12math@k12groups.org
private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org
newsgroup website: http://www.thinkspot.net/k12math/
newsgroup charter: http://www.thinkspot.net/k12math/charter.html

Date Subject Author
10/21/03 MB
10/21/03 Michael Hamm
10/21/03 Kevin Karplus
3/14/05 Fred