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THE ROLE OF CONSTRUCTIVE PROOFS IN ESTABLISHING EUCLIDEAN GEOMETRY THEOREMS

Zimvo Ndziba Yunivesithi Walter Sisulu, South Africa.
Benjamin Tatira Yunivesithi Walter Sisulu, South Africa.

Abstract

In the past, constructive proofs have been essential to the evolution of Euclidean geometry. Constructive proofs, as opposed to non-constructive arguments, give a way to construct geometric objects and hence clearly prove their existence. With a focus on their educational, philosophical, and mathematical value, this study explores the use of constructive proofs in proving Euclidean theorems. This study emphasises how constructive approaches not only improve the rigour of Euclidean geometry proofs but also aid in learners' mental comprehension of geometry. It does this by using a qualitative research methodology based on document analysis of classical and contemporary mathematical books. The results revealed that constructive methods strengthen critical thinking and problem-solving abilities by bridging the gap between abstract reasoning and real-world application. Additionally, this study argues that constructive proofs are essential to preserving the essence of Euclidean geometry, which is based on constructions with a straightedge and compass. This study has ramifications for mathematics education, namely in terms of encouraging learners to engage with geometry more deeply and offering models for curriculum creation that prioritise active learning and reasoning.

Keywords

Constructive Proofs, Deductive Proofs, Euclid, Euclidean Geometry, Logical Reasoning,