Measuring long distances with a 2600-year device: a historical application of Triangle Similarity by Thales of Miletus

Abstract

Triangle Similarity is a content from the last years of Middle School and first years of High School that elaborates on previously acquired notions of geometric proportions. Aiming to contribute alongside official document guidelines, a didactic sequence based on a historical account was applied, guiding students in the construction of an apparatus historically attributed to Thales of Miletus. Such a device would allow him to measure the distances of ships from the coast using Triangle Similarity. After proving its effectiveness in a miniature environment, the constructed device was applied to measure distant objects from the top of the school’s tallest building. An error analysis was carried out to encourage scientific reflection on the experiment. The project also included many connections with History and Arts during the discussions and crafting of the device. The classes were received with great enthusiasm by the students, who showed considerable understanding of the studied process.