Cissoide de Diocles: um pouco de história e aplicações em sala de aula

Abstract

This dissertation explores the Cissoid of Diocles, a remarkable mathematical curve, by examining its history, geometric construction, and properties. In particular, we investigate its connection to the problem of cube duplication, one of the classic challenges of Greek mathematics. The dissertation discusses the historical evolution of this problem, the impossibility of its construction using only a ruler and compass, and how the Cissoid of Diocles emerges as a geometric alternative for determining the cube root of 2. Beyond the theoretical approach, a didactic sequence designed for high school students is proposed, in which students manually construct the curve and use it to determine the side length of a cube whose volume is twice that of a given cube. Additionally, the GeoGebra software will be used to provide a more dynamic visualization of the Cissoid. The lesson plan is described in detail, including the geometric construction and the physical assembly of the cube using concrete materials, fostering a visual and experimental approach to the problem. Finally, the dissertation discusses the importance of this approach in mathematical education, exploring how historical geometric activities can be integrated into the modern curriculum to enrich students’ understanding of fundamental mathematical concepts.