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Virtual Reality

.....Make the effort of a download of about twenty minutes, which you will only do once and for all: the result is worth it. The "virtual reality" images are simply extraordinary, and you are the one who will "pilot" them. Yet the objects themselves download in ten or twenty seconds. Moreover, on this site, a whole section devoted to this virtual reality imagery will develop at great speed, thanks to the collaboration of a CAD professional, Christophe Tardy. So, sooner or later you will have to download Cosmo Player. Might as well do it now...

.- If Cosmo Player (free, downloadable utility) is already installed on your machine, go on to the next part: Read the "instructions for piloting" (unless you already know them), then choose an object and click on it.

...- If this shareware utility is not already installed on your machine, read the instructions for downloading it free of charge.

August 19, 2004: Received this message from a reader:

Hello,

On your Virtual Reality page (http://www.jp-petit.com/science/maths_f/virt_real.htm), the official Cosmo Player site no longer allows this Reader to be downloaded (File Not Found during download), so it is impossible to see the virtual representations on your site. Nevertheless, I found, with some difficulty, a site that still had this program; if readers have problems, you can pass on this link:

http://www.cs.iupui.edu/~aharris/vrml/ (Go down to the bottom of this page, in the Cosmo player section)

Geometric objects, do you then have a soul?

Collaboration with Christophe Tardy:

...Christophe, in his early thirties, living in Aix-en-Provence, was a little bored creating, in CAD, synthetic images of chemical complexes. The eversion of the sphere, which I described as early as '75 using drawings that will fry your neurons, has still only been understood by a very small number of people (article M.Morin J.P.Petit in January '79 in Pour la Science). Until recently, rare were the people who had seen a Boy's surface with their own eyes, and even fewer those who had been able to hold one in their hands, until I invented its representation with its system of elliptical meridians, then its polyhedral form, described in the Topologicon. If by chance you go to the Palais de la Découverte in Paris, you will find, in the center of "room p", a model of a Boy's surface that is finishing oxidizing. I do not know whether a little card has now been put somewhere to say that it was I who invented this representation; that would have pleased me. On my last visit, there was nothing. But, oh well....
... The journals La Recherche and Pour la Science having for fifteen years refused any article by me dealing with subjects of this kind, considered an illegal exercise of mathematics, I had ended up getting discouraged. Nor can it be said that the idea of producing new comic strips sold in black and white at 90 F each, when color comics can be found for less than 50 F, constituted a powerful stimulus. Such a stupidly dissuasive price was bound to put off my usual best-intentioned customers: high-school students, teachers and researchers, at least for this type of comic strip.
... The possibility of showing new creations on an Internet site rekindled my imagination. But coming across, at a street corner, a "country" that knows how to transform cardboard models in two shakes into objects inhabiting the world of virtual reality was a very pleasant surprise. You will find in what follows the result of this beginning of collaboration with Christophe. Many other objects will quickly be added to this list. He has made a fantastic film, in color, in which one strolls inside a Boy's surface, entering through one of its ears. He was thus the first to take this approach. We will put it on a cd. It is a little "heavy" to be made downloadable. But what a marvel....