An Archimedean research theme: the calculation of the volume of cylindrical groins

Starting from Archimedes’ method for calculating the volume of cylindrical wedges, I want to get to describe a method of 18th century for cilindrical groins thought by Girolamo Settimo and Nicolò di Martino. Several mathematicians studied the measurement of wedges, by applying notions of infinitesimal and integral calculus; in particular I examinated Settimo’s Treatise on cylindrical groins, where the author solved several problems by means of integral

Mathematical surfaces models between art and reality

In this paper, I want to document the history of the mathematical surfaces models used for the didactics of pure and applied “High Mathematics” and as art pieces. These models were built between the second half of nineteenth century and the 1930s. I want here also to underline several important links that put in correspondence conception and construction of models with scholars, cultural institutes, specific views of research and didactical studies in mathematical sciences and with the world of the figurative arts furthermore. At the same time the singular beauty of form and colour which the models possessed, aroused the admiration of those entirely ignorant of their mathematical attraction

Thought and Body. An activity of Logic in primary school

AbstractIn the recent decades, the pedagogical debate has been formerly traversed by the emergence an then by the assertion of a matured awareness on the importance of the psychomotor skills in the educational-didactic path. The interpretive bio-psycho-social matrix has today become one of the pivotal points on which the educational-didactic activity rests and develops for the training of child's personality in its full motor, mental, perceptual, emotional, sensory development. Pedagogues, educators, and training professionals are increasingly confident that, since the birth, children are sensitive to the stimuli and to the environmental intervention, therefore it's essential to know their growth allowing them to express their potential at the maximum possible level. Essential was the contribution given by Jean Le Boulch, who considering the individual in his entirety, stresses the importance of affectivity in the path of a motor, logical-communicative, psycho-physical maturity of the child (Le Boulch 2010).This guarantees the full functional development and the acquisition of a corporeal awareness, which is basic and indispensable, both in the path of space-time orientation and in the path of logical-conceptual acquisition. Within this theoretical framework, it has been thought of a teaching proposal which would combine all the highlighted points for a project that will promote the development of language and logical thinking. The project is addressed to pupils in the first classes of the primary school. The proposed subjects, directly recall the functions above mentioned. If we consider language and motion as instruments of thought, we suggest activities meant to supply children with a rich endowment which define certain aspects and elements of the surrounding and everyday actions.These activities will also translate emotion and perceptions in words. A child should be educated to communicate his experiences following the space and time landmarks, to describe objects, people and events. One should promote activities that help to organize logically events and circumstances. The path is articulated in different points:1.(First step of corporeal involvement) pupils altogether start to walk following a prearranged course; teacher, illustrating what they can see around, underlines certain points and objects.2.The second step occurs in the classroom: during a collective discussion, pupils will decide the benchmarks which will help them to recreate the path. Teacher's role will be to stimulate the discussion through questions on the features of the references chosen by pupils and on the features that don’t belong to them.3.The third step consists in the representation of references as drawings which will be reproduced in their description with affirmative and negative sentences; other questions will stimulate their perception of the body in a three-dimensional context. The questions could be: was the object at your right or at your left? In that point, have we turned to the right or to the left? Was that object before or after the other