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Surprising Geometric Constructions: Ancient Tools and Modern Technology

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Abstract

This article presents an innovative approach to enhancing mathematics teachers’ professional development. It focuses on geometric construction using only ancient drawing tools: an unmarked ruler, a pencil, and dynamic geometry software. Six construction tasks are introduced. These demonstrate how limited tools can foster deep geometric understanding, creative problem-solving, and pedagogical growth. The study addresses the need for improved geometry instruction. It challenges teachers with constructions that mirror the work of ancient mathematicians, using GeoGebra applications. These dynamic applications support inquiry-based learning, enable the exploration of geometric properties, and provide scaffolding for complex tasks. The presented tasks are designed for both pre-service and in-service mathematics teachers. They aim to expand teachers’ geometric, technological, and pedagogical knowledge, while also promoting critical reflection and creative thinking. This approach enriches teachers’ understanding of Euclidean geometry and equips them with innovative methods to inspire students. Teacher educators are encouraged to implement these tasks and explore the knowledge development that emerges during individual and collaborative problem-solving processes.

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Correspondence to Ruti Segal, Moshe Stupel or Avi Sigler.

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Segal, R., Stupel, M. & Sigler, A. Surprising Geometric Constructions: Ancient Tools and Modern Technology. Reson 31, 287–301 (2026). https://doi.org/10.1007/s12045-026-1945-z

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  • DOI: https://doi.org/10.1007/s12045-026-1945-z

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