[math-fun] e^(iπ)
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.
Clearly the second. 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. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- -- http://cube20.org/ -- http://golly.sf.net/ --
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. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Thane Plambeck tplambeck@gmail.com http://counterwave.com/
I'm firmly in the exp(i pi) = -1 camp.
Sent: Saturday, January 19, 2019 at 2:44 AM From: "Thane Plambeck" <tplambeck@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] e^(iπ)
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. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Thane Plambeck tplambeck@gmail.com http://counterwave.com/ _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Thane Plambeck tplambeck@gmail.com http://counterwave.com/ _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Thane Plambeck tplambeck@gmail.com http://counterwave.com/ _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
"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" 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. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Thane Plambeck tplambeck@gmail.com http://counterwave.com/ _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
I've always gone with e^(iπ) + 1 = 0. Not only does it have the five fundamental constants, 0, 1, e, π, i It also uses the three fundamental operators +, *, ^
-----Original Message----- From: math-fun [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Bill Gosper Sent: Friday, January 18, 2019 9:12 PM To: math-fun@mailman.xmission.com Subject: [math-fun] e^(iπ)
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. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
e^(iπ) = -1 tells us "A 180-degree turn points you in the opposite direction" e^(iπ) + 1 = 0 tells us "A 180-degree turn gets you back where you started"
-----Original Message----- From: math-fun [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of David Wilson Sent: Saturday, January 19, 2019 12:26 AM To: 'math-fun' Subject: Re: [math-fun] e^(iπ)
I've always gone with e^(iπ) + 1 = 0.
Not only does it have the five fundamental constants, 0, 1, e, π, i It also uses the three fundamental operators +, *, ^
-----Original Message----- From: math-fun [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Bill Gosper Sent: Friday, January 18, 2019 9:12 PM To: math-fun@mailman.xmission.com Subject: [math-fun] e^(iπ)
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. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Who's the audience, and what is the message to be conveyed? Both seem pleasing in their own way. On 1/18/19 18:11 , Bill Gosper 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. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Which is more beautiful? a_n x^n + a_{n-1} x^{n-1} + ... + a_1 x = - a_0 or a_n x^n + a_{n-1} x^{n-1} + ... + a_1 x + a_0 = 0 ? On Fri, Jan 18, 2019 at 7:12 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. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike https://reperiendi.wordpress.com
participants (10)
-
Adam P. Goucher -
Allan Wechsler -
Andres Valloud -
Bill Gosper -
Cris Moore -
David Wilson -
Mike Stay -
Neil Sloane -
Thane Plambeck -
Tomas Rokicki