Again from the pedagogic viewpoint: gosper.org/eiπ.png What is this adding 1 garbage? —rwg Mandelbrot once told me of a French math department which routinely discouraged explicit equations. Disembodied expressions were all implicitly 0. A visiting government inspector: "I don't understand. If everything is zero, why do you need all this grant money?" On Fri, Jan 18, 2019 at 10:57 PM Bill Gosper <billgosper@gmail.com> wrote:
-------- Original Message -------- Date: 2019-01-18 21:19 From: Neil Sloane <njasloane@gmail.com> Reply-To: math-fun <math-fun@mailman.xmission.com>
Adam Goucher wrote: "I'm firmly in the exp(i pi) = -1 camp."
Me too, there is no argument. "Beauty is truth" is obviously better than "beauty - truth is zero" ---------- When I first saw e^(iπ) + 1 = 0, I gagged. If you like clutter, why not throw in a factor of GoldenRatio? But now I have a clincher. I asked a beginner to solve x^x = e^-(π/2), with the hint: "Try taking √ of the World's Most Beautiful Formula." He used the messy one and got stuck! —rwg (I actually asked for *two* solutions.)
On Fri, Jan 18, 2019 at 10:05 PM Cris Moore <moore@santafe.edu> wrote:
but those just imply e^(i pi) is +1 or -1.
On Jan 18, 2019, at 7:53 PM, Allan Wechsler <acwacw@gmail.com> wrote:
Nobody for e^(2iπ) = 1 or e^(2iπ) - 1 = 0 ?
On Fri, Jan 18, 2019 at 9:45 PM Thane Plambeck <tplambeck@gmail.com> wrote:
The second one is more aesthetically pleasing, but the first one seems (weirdly) more directly informative somehow, to me.
On Fri, Jan 18, 2019 at 6:12 PM Bill Gosper <billgosper@gmail.com> wrote:
At the risk of a protracted and rancorous political dispute, I'd like an informal vote on which is most "beautiful": e^(iπ) = -1 or e^(iπ) + 1 = 0 ? —rwg I get polarized just thinking about it. _______________________________________________
A wisecracking eavesdropper alleged I was polarized from only turning halfway around, trying to revive the 𝛕 abomination e^(i 𝛕) := 1, not q^(1/π). Well, a 2π rotation still leaves my neutrons polarized!