A few years ago Benoît Mandelbrot, a precursor to Fractal Geometry, noticed fractal featuresinvariouspartsofnature(suchasclouds,relief,trees,plantsandrivers),thehuman body, geometric figures and computer constructions. From this, fractals can be studied and systematized into their own geometry - a Geometry Fractal - and, as a consequence oftherelevanceofthediscoveriesaboutthem,thesegeometricobjectssufferedwithgreat scientific value. Therefore, we present here a proposal of approach of Fractal Geometry in Basic Education. This proposal consists of actions that insert elements of Fractal Geometry in high school mathematical contents to display or fix concepts. Thus, the purpose of this proposal is the inclusion of this new Geometry in High School, as a tool for teaching mathematical materials, in view of the possibility of this action to enhance the learning of mathematics, the most significant use for students. To do so, ask for a little history of geometry, teaching of geometry in Brazil and fractal geometry, trying to identify their origins and understand the context of the treatment. Through bibliographical and exploratoryresearchmainlyinBoyer(1996),Valente(1999),Pavanello(1993),Barbosa(2005), Janos (2008) and Smole and Diniz (2016), they record the history of geometries until the insertion of Geometry. High School Fractal. As a consequence of the studies, we realize that the Geometry Fractal offers wide scope for application in Basic Education, from the visual appeal to the formation of patterns, which are important for the development of reasoning and lead to solutions of some mathematical problems.
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