Rettangoli grigliati. Riflessioni tra isoperimetrie in diversi contesti di apprendimento

Abstract

The “grilled rectangles”, namely brectangles drawn in a grid, have a perfect coincidence with the rectangles obtained by moving a tight string between the thumb and forefinger of the two hands proposed by Emma Castelnuovo. From this movement, which has been reproduced on squared paper during the workshop, many questions arise: how many of them are there? Do the perimeter and area of ​​these rectangles vary? What unit of measurement do we choose? For the perimeter it is unique. Instead, for the area we have more choices. What does this fact entail? The rectangles drawn in grids of different sizes are then analyzed. The various data are calculated, tabulated and compared. Why is the perimeter always an even number? Why is the area not always an even number? When does the square form? In conclusion we look for a regularity and we try to find a formula that generalizes it. The activity is exciting at any age and allows you to introduce, or consolidate, the concepts of isoperimetry and equivalence.