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L’histoire de la forme est un concept complexe qui remonte à l’antiquité grecque, tout au long de cet article nous aborderons différentes facettes de ce concept dans le cadre particulier de la géographie. Nous développerons différentes perspectives sur la forme en géographie et sur son ontologie « locale ». Nous verrons également comment ce concept a été abordé, en géographie physique, en géomorphologie, en tenant compte de divers moments historiques et des cadres scientifiques successifs. La géomorphologie servira de laboratoire physique pour approfondir la notion de forme en géographie. Dans cette recherche nous croiserons des concepts de penseurs de différentes époques tels que Goethe, D’Arcy Thompson, Prigogine, mais surtout, René Thom et Benoît Mandelbrot, penseurs qui nous ont offert les outils pour concevoir une vision renouvelée de la forme en géographie.

Quality of the cutting machining process of martensitic steel is analysed as a function of the cutting speed. This analysis is performed by topographical measurement of tooled surfaces. A statistical analysis taking into account more than hundred roughness parameters allows us to prove that the mean slope value of the profile is the best parameter to characterise the cutting speed effect on the surface topography. This roughness parameter discriminates the cutting speed threshold between two cutting stages and moreover, discriminates also the cutting process in each stage (the usual Ra parameter is unable to do it). A mathematical treatment based on the chaos theory is then processed. From the profile of the machined surface, a two-dimensional attractor is constructed. Thanks to an original method, it is shown that this attractor depends on two mathematical functions: the first one characterises the work hardening during the cutting process and the second is related to thermal softening. For a critical cutting speed, these two mechanisms are linked together and lead to a single attracting final state. This stage is governed by generalised work hardening. Above this critical speed, the attractor will present a two branches bifurcation, which means that the cutting process is now alternating between the two different states. This chaotic mode is related to the instability between work hardening and thermal softening. This instability is confirmed by a fractal analysis based on the reconstructed profiles from the attractor : the higher the cutting speed, the higher the fractal dimension. [ABSTRACT FROM AUTHOR]