Récréations mathématiques, géométrie de situation... De nouveaux outils pour enseigner les mathématiques à la fin du XIXe siècle

International audienceAt the end of the XIXth century, some mathematicians like Charles-Ange Laisant (1841-1920) or Édouard Lucas (1842-1891) develop new ideas about teaching mathematics using innovative tools or original visualizations. These ideas are linked to their interest for recreational games viewed through a mathematical background and other specific problems including combinatory, number theory, algorithms and the “géométrie de situation”... They are studied especially in L'Arithmétique amusante (Lucas, 1895) or the Initiation mathématique (Laisant, 1906), two books addressed to educators in a large sense. We propose to give some examples of these mathematical representations and these ingenious games, explicitly presented by their authors in a didactical scheme. Thus, we talk in particular about : - “l'éventail mystérieux” proposed in order to introduce binary computation - “le vol des grues” and other drawings proposed in order to give visual proofs of particular sums of integers - a singular representation of decomposition of integers into prime numbers using paths in specific drawings - graph of functions, especially linear ones, where pupils can see solutions of meetings problems - the use of chessboards in combinatory and so on... Moreover, several of these approaches could be presented nowadays to students of secondary schools. We discuss the role of visualizations through these experimentations and point out the connections between diagrams and symbolisms. We study the need of arousing curiosity through striking results in order to present new mathematical notions. We also underline the goals of representing processes in certain moments of mathematical learning and the generalizations enabled by many of these presentations, much more than simple recreational questions.</p

Nouveaux outils et ressources numériques en bibliothèques

Cette journée professionnelle a été organisée par le groupe ABF-Aquitaine à l’initiative de la Bibliothèque municipale d’Anglet. Il s’agissait de dépasser les propos généraux pour livrer les premiers bilans de projets concrets mis à l’essai dans des contextes contrastés

"Et nous, et nous… ?"

Quand ils pensent « presse », les bibliothécaires pensent généralement régionale, voire nationale, et aux différents médias… Et ils omettent de la presse qui leur est spécialement dédié : celui de la presse professionnelle. Que peut-on attendre d’elle ? Nous avons posé la question à deux contributeurs de Bibliothèque(s)

La censure au placard

Courroie de distribution du livre en zone rurale, service public sans usagers directs, la BDP est le lieu d’une réflexion accrue sur la question de la censure et de l’autocensure : le non achat y prend une signification particulière. Angoisse d’un bédépiste au moment de la décision

Simulación de campos aleatorios espacio-temporales utilizando un filtro de Kalman modificado

ResumenUn campo aleatorio espacio-temporal es un modelo probabilista utilizado para representar fenómenos que, además de variar espacialmente, cambian con el tiempo. Este tipo de modelo es de gran interés práctico en ingeniería porque permite representar fenómenos transitorios y generar configuraciones o imágenes de la distribución de un atributo o variable condicionado a observaciones temporales. En este artículo se propone una formulación alternativa de una variante del método EnKF (Ensemble Kalman Filter) (Evensen, 2007) basada en conceptos comunes en geoestadística y explica con detalle su desarrollo numérico. La utilidad del método se ilustra resolviendo un problema de flujo de agua transitorio en un medio poroso aleatorio completamente saturado.AbstractA spatiotemporal random field is a probabilistic model used to represent phenomena that, besides varying spatially, evolve in time. Such kind of model is of great interest in engineering for representing transient phenomena and generating configurations or images of the distribution of an atribute or variable conditional to temporal observations. In this paper an alternative formulation of a variant of the EnKF method (Ensemble Kalman Filter (Evensen, 2007) based on concepts commonly used in geostatistics is proposed and its numerical implementation is explained in detail. The benefits of the method are illustrated by solving a transient flow problem in a fully saturated random porous media

On-site assessment of methods to measure gaseous emissions from biological treatment of waste

International audienceLandfilling of biodegradable waste must decrease to fulfil the Council Directive 99/31/EC on landfills, in order to reduce the emission of gaseous and liquid pollutants during the landfill lifetime. Therefore, pre-treatment of the organic fraction of municipal waste prior to landfilling is being developed in several countries. In France, the organic fraction is either separated and treated through selective collection of biowaste, or through mechanical sorting in the plant followed by biological treatments (anaerobic or aerobic), the refuses only being landfilled. Or the mixed waste is stabilized by an aerobic process before landfilling. These different processes emit gases which may be harmful for health or the environment (toxic, explosive, odorants, greenhouse gases...). Some of the emissions can be collected and treated through biofilters, while other gases are emitted by surfaces (typically, compost windrows) and cannot be collected unless they are enclosed. Also, the efficiency of the biofilters must be assessed. IRSTEA and INERIS have been working together for several years on the use, comparison and improvement of surface emission measurement methods, applied to biological treatment plants of solid waste. Gaseous emissions were studied on: composting process of pre-sorted organic matter from mixed waste, with a small or larger mesh and porosity, in either turned or aerated windrows, on biofilters, and on landfills which are located beside the composting plants. Depending on the ventilation air flux, different measurement methods were used: static (accumulation), dynamic or chimney type chambers, and a total cover of a biofilter with a plastic tarb. Several of these measurements were undertaken in order to evaluate the global gaseous emissions from those sites, to provide data to an environmental technology validation exercise (ETV). Measurement campaigns presented here comprise: comparison of fluxes measurement techniques, calculation of gas fluxes (CO2, CH4, NH3 and N2O) emitted from composting windrows and biofilters, calculation of biogas emission (methane + CO2) before and after a final cover was set on a landfill. Comparisons of the two first chambers have been made since 2007 on several sites (composting of the organic fraction of municipal solid waste or stabilization prior to landfilling). On the first site (non aerated windrows and small mesh) the difference between the measured fluxes was a factor of 2. This factor is rather small: differences between flux measurements using different devices can lead to differences as large as a factor of 100. More recent tests, presented here, show a better agreement: the difference between the two techniques lies within the measurement uncertainty. Comparison of surface air speed measured by two different chimney chambers lead to comparable results. During one experiment, the global air flow interpolated from chamber data was underestimated compared to input flow measurement, because of preferred pathways of the air flow along the wall of the biofilter. When the border effect is correctly taken into account, the total gas flow measured with the chimney chamber and the one measured by a total cover of the biofilter show a good agreement. Biogas surface emissions were measured with the static chamber, on a landfill which receives biologically stabilized waste. This landfill was partly uncovered, so only a part of the biogas was collected and flared. After the final cover was installed, the total biogas flow which was collected and flared was comparable to the sum of (the surface emissions + the collected biogas) without the total cover. The results presented here show that on different sites, different emission measurement methods were used, and that generally there is a good agreement between the methods, providing the care of use are respected. Advantages and care of use for the different methods, depending on the aeration conditions, have been established and some recommendations are given

Empreintes d’échanges au sein de la Société mathématique de France dans les pages de son Bulletin : le cas de Charles-Ange Laisant

La Société mathématique de France (SMF) créée en 1872 pour promouvoir les travaux des mathématiciens français accueille rapidement le polytechnicien Charles-Ange Laisant (1841-1920) qui s’investit par ailleurs dans de multiples communautés savantes à la fin du xixe siècle. Son implication durable, ses itinéraires d’administrateur et d’auteur permettent, à partir des renseignements fournis par le Bulletin de la SMF, une approche originale de la circulation de ses travaux au sein de la Société. Une étude des comptes rendus de séances met en lumière tant sa production d’écrits mathématiques proprement dits que ses interventions orales sur des sujets variés lors de ces réunions. L’exemple de celui qui sera président de la SMF en 1888 offre ainsi une perspective particulière sur les mathématiques discutées lors des réunions de la Société, sur les liens qui se tissent avec d’autres cercles savants ou sur les réseaux et collaborations ponctuelles à l’intérieur même de la SMF.The Société mathématique de France (SMF) was created in 1872 to promote the work of French mathematicians. Charles-Ange Laisant (1841-1920) quickly joined the society while also contributing to the work of many other academic communities in the late nineteenth century. His long-term involvement within the SMF as an administrator or an author enables an original approach to the circulation of his work within the Society based on information given in the SMG Bulletin whereas the minutes published therein shed light on both Laisant’s own mathematical production and his spoken contributions on various topics during the society’s meetings. The example of Laisant, who was elected president of the SMF in 1888, offers an original standpoint on the topics discussed during the society’s meetings, on the relationships established with other scientific networks and on occasional collaborations within the SMF

Geotechnical Zoning of Mexico Valley Subsoil

AbstractA new geotechnical zoning map for the subsoil of Mexico Valley is presented. This proposal is based on a Geographic Information System for Geotechnical Borings (GIS-GB), which contains over 10000 soil profiles. In addition to the geotechnical information, available topographic and geological data on the studied area were taken into account. Geostatistical techniques were used to assess the spatial distribution of the thickness of the lacustrine clay deposits within the area down to the so-called deep deposits. As a result, a contour map was obtained that was used to update the current geotechnical zoning map for Mexico Valley. It has been proposed to include this new map into the Building Code for the Federal District (Mexico City)