pic
 
MATHÉMATICS & ARTS
Exhibit & Lecture
Initialy presented at the Institut Henri Poincaré, Paris. France.
January 22 - June 30, 2005
francais   english
APÉRY François
Mathematician

Former student of l' École Normale Supérieure de Cachan and lecturer at the University of Alsace, François Apery passed his thesis in differential topology under the direction of Bernard Morin . He is pursuing his research in geometry and in small dimension topology. Apery likes to realize objects and three dimensional figures of mathematical objects.

 

The models exhibited here are of two surfaces, respectively called "Surface of Boy" and "Closed central Model". The principle of their realization rests on one hand in the need to represent a geometrical object as exactly as possible, i.e. by accurately respecting the algebraic data resulting from the equations which define it, and to exploit certain degrees of freedom to accentuate its aesthetic qualities, even if they remain subjective. Among these degrees of freedom are the choice of the scale, the proportions and the choice of materials.

A quality extended to the surfaces generated by other families of curves starting with the conical ones like the ellipses, by using the mechanical properties of a metallic wire of piano wire type. Its elasticity results in the fact that it does not keep trace of the deformations it undergoes, provided the tension is not too important. A wire of given length subjected to constraints finds a position of balance materialized by a curve. If for example, one forces the ends to meet at a given point according to a flat angle representing four constraints, the position of equilibrium is a circle. If one can force the wire to pass by a second point of the plan of the circle and create a fifth constraint, the wire finds its balance as a plane curve which will be convex and not un-similar to an ellipse. It brings the idea to create a surface generated by ellipses using a frame on which steel wire are assembled and set to satisfy at least five conditions. As in "Surface reglees" the surface represented this way will give the impression to exist only virtually by the means of its apparent contours.

One should notice that those are stand-alone models created without screws, bolts or welding, and are entirely dismountable. One could project what a monumental construction it could become, knowing how much architecture draws from regulated surfaces. Those structures are waiting for their architect...

Click thumbnail to  enlarge picture

The starting point is to demonstrate the construction of surfaces known as regulated. The displacement of rectilinear right-hand sides on these surfaces makes it possible to generate them entirely. The model of such type of surface is created by a frame intersected by wires materializing the generating lines and forms. One of the attractions of these models is that their surface is not carried out in its entirety, unlike opaque wood, plaster or even latticed models. Its surface appears often only by its apparent contour which seems to float in space a little like a hologram obtained by the reflection of the light.

Each one of the two models is generated by a family of ellipses passing by a fixed point. The tangent of each ellipse is fixed in the beginning and the ellipse has to pass by two points of a certain line materialized by a metallic surface. The model's assembly requires a reinforcement made up of an horizontal base and a vertical stem to maintain the metallic part in place. At this point in time the mechanical properties of the steel wire balances the tensions, the reinforcement becomes useless, and the metal part seems suspended in levitation. It demonstrates the effects of apparent contour of regulated surfaces.

 
HOME INTRODUCTION PROGRAM GALLERIES CONTACT
 
 
Copyright © 2005 -2006. Hermay NM