Albion College Mathematics and Computer Science Colloquium

Title: Spherical geometry: The oldest example of a non-Euclidean geometry
Speaker:Celso Melchiades Doria
Departamento de Matemática
Universidade Federal de Santa Catarina
Florianópolis - Santa Catarina, Brazil

It will be introduced some historical aspects of Geometry, the formula for Pythagoras' Theorem on the surface of a sphere and also some metric relations (cosine and sine laws). As a by product, the well known Pythagoras' Theorem from Euclidean geometry will be obtained. Spherical geometry has been part of humankind since the rest beginning of navigations through the seas. Thus, since then, the measurement of distances and the description of positions on the surface of Earth have been essential. The GPS at those old years were the stars, the geographical points and later the lighthouses (Alexandria Lighthouse was the most famous one). The Pythagoras' Theorem, on the surface of a plane, has been known for a very long time as one of the most important tools to measure distances and angles, but unfortunately it could not be applied to measure distances and angles for the purpose of navigation. So, how much Geometry was used for the purposes of navigation? Answer: A LOT. Although the question concerning the 5th-Euclidean postulate took around 2000 years to be settled, it could had been settled centuries before if sailors and mathematician were acquainted with the fact that over the surface of a sphere the concepts of Geometry could also be defined and further developed. The main problem was, until 1820, nobody knew how to define a Geometry, it was wrongly thought that Geometry meant Euclidean Geometry (Kant argued that the truths of geometry were synthetic a priori truths, and not analytic).

Location: Palenske 227
Time: 3:10 pm

author  = "{Celso Melchiades Doria}",
title   = "{Spherical geometry: The oldest example of a non-Euclidean geometry}",
address = "{Albion College Mathematics and Computer Science Colloquium}",
month   = "{12 February}",
year    = "{2009}"