The present essay presents a production carried out in the field of plane and spatial geometry; takes an
approach to optimizing mathematical learning implemented by technological tools that provide a greater scope of assimilation of concepts and speed up the internalization process. It shows an example using the Geogebra application in the production of all the images that illustrate the applications of the content, and highlights the performance of this software in achieving the goals proposed in the objectives of this work, as, with the capacity and good teaching of the application, it was possible to fulfill the three specific objectives, namely: building the entire production of graphics, surfaces and solids of revolution - where the reverse surface of the sphere was generated; develop the processing of squaring regular polygons, as well as squaring the circle only using a compass and a non-graduated ruler; present a geometric demonstration of the Pappus Guldin Theorem of the area and make some applications of the theorem. In the topic of quadratures, the polygons, from the triangle to the heptagon, had their quadratures fully elaborated, and the circle achieved a very simple approximation; and, also, a graphical construction was developed for the rectification of the circumference that can be reproduced with a compass and non-graduated ruler, in a simple way and that gives a good approximation to two decimal places for the number π. The demonstration of Pappus Guldin’s Theorem, the last topic, allows us to visualize the entire mechanism of movement in the formation of objects and perceive the ingenious idea applied in the procedure for calculating their area, which applies concepts ofmovement dynamics in a simplified formula. The visual support of the multicolor images of geometric figures produced by the application also stands out, in order to provide a more playful reading for the reader’s journey, from the beginning to the last topic.
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