Limitations of Euclidean geometryĮuclidean geometry has limitations, particularly because it is not possible to study a three-dimensional space where the fifth postulate of Euclid is not fulfilled.Īlbert Einstein drew attention to the need to resort to non-Euclidean geometry to study curved space-time, that is, one that is not linear (as is traditionally conceived).
Euclid’s fifth postulate tells us that if a line intersects two others and forms, on the same side, two acute interior angles (less than 90º), those two lines prolonged indefinitely intersect from the side on which those angles are (see lower image).Īs we can see in the figure above, if line A and line B extend upwards, they intersect.All right angles are congruent, that is, they have the same measure (90º).It is possible to draw a circle centered at any point and of any radius.Any segment can be continuously extended in either direction.Given two points, a line can be drawn connecting them.The five postulates of Euclid are the following:
That is, although they are often confused, plane geometry is only one part of Euclidean geometry that is dedicated to the study of geometric figures in a two-dimensional plane. Even from Euclidean geometry, three-dimensional figures can be analyzed, as long as Euclid’s postulates are fulfilled (which we will detail later), in particular, the fifth of them.
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