lambert@boring.UUCP (03/15/85)
> Define an "exponent dual" of the x to be some OTHER number y so that > x^y = y^x An amusing problem concerning exponent duals: Define a real function f such that i) for each z <> 0, the exponent dual of f(z) is f(-z); ii) all exponent duals can be obtained in this way; iii) the expression defining f(z) is closed and analytic (that is, is built from standard mathematical operations and functions; no limits or infinite sums). Solution (rot 13): Gur inyhr bs gur shapgvba s nccyvrq gb m vf: rkc bs {m bire [(rkc bs m) zvahf bar]}. Gur cnve (gjb, sbhe) vf bognvarq ol gnxvat m = +/- 0.693147180559945 -- Lambert Meertens ...!{seismo,philabs,decvax}!lambert@mcvax.UUCP CWI (Centre for Mathematics and Computer Science), Amsterdam
bulko@ut-sally.UUCP (William C. Bulko) (03/16/85)
[ bug off! ]
It was interesting seeing this problem haunt me again. When I was a freshman
majoring in math, I took my first CS course (in FORTRAN) and struck up a
"protege" relationship with my professor. One of the research projects he
later assigned me involved studying a multiple-precision package available
on the university's computer to aid in a computer solution to this very same
problem. I played around with a mathematical approach to the problem
(behind his back) and came up with a complete solution and some interesting
graphs! Eagerly, I presented the stuff to him -- and he smiled, saying,
"That's pretty good! Here, take a look at this." He then handed me the
first draft of an article one of his colleagues was writing about the
problem, containing all of which I had done, times 10 -- an a footnote
acknowledging that Euler had done all of this years ago.
I still have that draft of the article. Perhaps that incident was
one of the driving forces that made me shift to computer science in grad
school.
--
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"To err is human; to admit it is not."
Bill Bulko Department of Computer Sciences
The University of Texas {ihnp4,harvard,gatech,ctvax,seismo}!ut-sally!bulko
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