![]() ![]() Then, the book goes on with the statement of the postulates, including the famous Euclid’s fifth postulate, which original statement is: Looking at these three objects, we already see that the Ancient Greeks restricted their studies to flat figures, ignoring different type of surfaces. The basic elements are: the point, with is considered the element with no dimension the segment of line, which is the object with only one dimension and the plane, which has two dimensions. The first book starts by enouncing the basic elements of geometry and the celebrated five postulates. The main legacy of the knowledge developed in Ancient Greece on these topics are the 13 books of the Elements by Euclid. In the Ancient Greece, these questions gave rise to a rational, abstract discipline where statements were originated in a deductive way, with the exemption of few axioms, considered too fundamental to need proves. ![]() ![]() Its development originate from some real-world problems about the measurements of fields and territories. Geometry is traditionally the branch of Mathematics that studies shapes and spatial relationships of bodies. In fact, geometry on the sphere is surprisingly different from the one on the plane: for example, Pythagoras’ Theorem does not hold anymore! Here, we will present a version of Pythagoras’ Theorem for the sphere and we will show what links it has with the original one. In this post, we present some basic facts about the study of geometry on spheres. ![]()
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