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Topic: [HM] Dedekind versus Russell
Replies: 13   Last Post: May 10, 2003 1:34 PM

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Alfred Ross

Posts: 56
Registered: 12/3/04
[HM] badly sketched figures
Posted: May 2, 2003 11:10 PM
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Ralph A. Raimi <> wrote:

<< I have heard somewhere that Poincare said that geometry was
the art of reasoning well upon badly sketched figures. Does
anyone have a source for this? >>

See below :


Date: Sun, 16 Apr 2000 12:09:46 -0300
From: Julio Gonzalez Cabillon <jgc@ADINET.COM.UY>
Subject: Re: [EDUMAT] Cita sobre Geometria

A las 06:42 p.m. 15/04/00 +0200, Anna M. Vaello escribio:

| No se donde ni cuando lei una cita sobre Geometria que
| decia mas o menos: "La Geometria consiste en razonar
| sobre lo que no se sabe dibujar". Queria contarsela a
| mis alumnos, pero antes me gustaria saber las palabras
| exactas y quien fue el autor. Le suena a alguien mas?


La frase es de origen desconocido. Hasta donde yo se,
quien primero aireo esta cita fue Henri Poincare. Aparece
ya publicada en el Prefacio de su _Analisis Situs_ de 1895.

"Se ha dicho muchas veces que la Geometria
es el arte de razonar correctamente sobre
figuras incorrectas; pero, a fin de no caer
en error, estas figuras deben satisfacer
ciertas condiciones."

Poincare vuelve a referirse a esta idea, con otras
palabras, en el Cap. III (Pourquoi l'espace a
trois dimensions) de su "Dernieres Pensees"
[Bibliotheque de philosophie scientifique, Paris:
Flammarion, 1913], obra postuma. Hay traducion al
castellano de este clasico de Poincare [*].

Bastante tiempo despues, George Polya en su "How
to solve it" (p 208) menciona al pasar algunas frases
llenas de buen sentido de humor, entre las que se
encuentra la que tu buscas:


popular legend is absentminded. He usually
appears in public with a lost umbrella in each
hand. He prefers to face the blackboard and
to turn his back on the class. He writes $a$,
he says $b$, he means $c$; but it should be
$d$. Some of his sayings are handed down from
generation to generation.

"In order to solve this differential
equation you look at it till a solution
occurs to you."

"This principle is so perfectly general
that no particular application of it is

"Geometry is the art of correct reasoning
on incorrect figures."

"My method to overcome a difficulty is
to go round it."

"What is the difference between method
and device? A method is a device which
you use twice."

After all, you can learn something from this
traditional mathematics professor. Let us hope
that the mathematics teacher from whom you cannot
learn anything will not become traditional.


Poincare Henri: "Ultimos pensamientos", Coleccion Austral,
Edicion Espasa-Calpe Argentina S.A., Buenos Aires, 1948.

Desde un soleado Montevideo, recibe saludos de
Julio Gonzalez Cabillon

--Al Ross

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