The mathematics of the curves on the wall of the Colégio Arquidiocesano and its mathematical models: a case for ethnomodeling.

Abstract

In this article the authors share the results from conversation during a morning walk with students along a street in Ouro Preto. The simple observation that a phenomena one might see everyday may possess mathematical potential became an interesting debate topic that turned this observation into an exploration of the mathematics inherent in common architectural details. There are many similar conversations and situations in any city that can be used to encourage conversation, develop models and explore the relationships between mathematical ideas, procedures, and practices. The authors studied the mathematical models derived from curves along the wall and sought to verify if they were related to exponential, parabolic, or catenary curves. In order to make the necessary arguments to support these conjectures, models were elaborated and analyzed, and discussed through a methodological procedure in which some curves were randomly selected from the wall of the school. After examining the data they came to the conclusion that the curves on the wall approximate that of a catenary curve.