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From: Matt on 17 Mar 2010 18:08
I found mention of the following in _Geometry, A Comprehensive Course_,
by Dan Pedoe, 1970. The following is a google translation:


> Joseph Caron, professor of descriptive geometry and Chief "graphic works" in mart beginning of the century, the student met Henri Lebesgue in 1897 and he mentions in a footnote on page of his lectures on construction geometric [4, p. 210]:
> [...] Least, he has contributed to the love of geometry for many students, and this at a time when eminent scholars, endowed with great talents geometric tried never to reveal the simple ideas that and were guided to their results depend elegant general theory of abstract, which often only applied in specific cases in question. Geometry becomes a study of algebraic equations, differential and partial, and she lost the charm it needs to being an art, and almost a fine art.
>
> [4] Henri Lebesgue, Lectures on geometric constructions. Gauthier-Villars. 1950
>
> TRIBUNE LIBRE, collection of mathematical models of the library of the IHP, Jean BRETTE (Palace of Discovery)
> SMF - Gazette - 85 July 2000
> � Cyrile Cambon


I guess Caron is saying that as a student he preferred Lebesgue's
instruction, which included graphical approaches rather just the
presentation of equations.

I wonder what is the current practice of instruction in college geometry
in this regard, in say the US and Europe.

I think in the US, college geometry is taken mainly by future high
school math teachers. I get the impression it isn't taken much by
future math grad students, but I could easily be wrong about that.

So please try to describe how college/university geometry instruction
goes nowadays, who takes it, how rigorous it is, how graphical it is,
how it should be changed, whether it is better or worse than before, etc.


> Joseph Caron, professeur de g�om�trie descriptive et chef de � travaux graphiques � � l�ens au d�but du si�cle, que l��l�ve Henri Lebesgue rencontra en 1897 et qu�il �voque dans une note de bas de page de ses Le�ons sur les constructions g�om�triques [4, p. 210] :
> [...] et surtout, il a contribu� � faire aimer la G�om�trie � de nombreux �l�ves, et cela, � une �poque o� des savants �minents, dou�s de grands talents g�om�triques, s�effor�aient de ne jamais d�voiler les id�es simples qui les avaient guid�s et de faire d�pendre leurs r�sultats �l�gants d�une th�orie g�n�rale abstraite qui, souvent, ne s�appliquait que dans les cas particuliers en question. La g�om�trie devenait une �tude des �quations alg�briques, diff�rentielles et aux d�riv�es partielles ; elle perdait ainsi tout le charme qu�elle doit au fait d��tre un art, et presque un art plastique.
>
> [4] Henri Lebesgue, Le�ons sur les constructions g�om�triques. Gauthier-Villars. 1950
>
> TRIBUNE LIBRE, La collection de mod�les math�matiques de la biblioth�que de l�IHP,Jean BRETTE (Palais de la d�couverte)
> SMF � Gazette � 85, Juillet 2000
> �Cyrile Cambon
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