Geometria esférica e o relógio de sol

Abstract

In this work we present some elements, definitions and theories of Spherical Geometry that will be necessary for its understanding. We found that some results are different when compared to Euclidean geometry, such as the sum of the internal angles of a triangle. Just as in Euclidian Geometry there is a Trigonometry, Spherical Geometry also has its own, which is called Spherical Trigonometry. We present the Theorems and relations of Spherical Trigonometry that are fundamental for the calculations of the hour angles of the sundial. In relation to the sundial, we present the theoretical arguments necessary for its construction, its positioning and its correct reading . We show step by step how to build and read the Horizontal Sun Clock in any location in Brazil and the materials needed for this construction. Finally, we suggest an activity to be applied to elementary school students from the 9th year, in which we propose to explore some similarities and differences between Euclidean and Spherical Geometries using manipulable materials.