In the second decade of the nineteenth century, Gauss began to record and discuss his sense of the futility of continuing to try to prove the fifth postulate.
The following is excerpted, with permission of the publisher, from The Fifth Postulate Yet the success of their failures would reveal a whole new geometry and description of space and time.Įuclid’s fifth postulate: If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles. Therefore many mathematicians since the time of Euclid attempted to determine this redundancy without success.
However, the fifth postulate appears as though it should be a consequence of the others and hence redundant to be stated as a fundamental postulate. All but the last are straightforward and simple. He stated 5 postulates that act like a constitution for laws of geometry. With such a program, all geometric facts are the result of these postulates. Euclid began by introducing fundamental geometric ideas in Book One as definitions and postulates. It described the nature of mathematics in a way that wouldn’t be fully understood until the 20th century. However, his monumental work of 13 books called The Elements achieved something far more than a list of geometric facts. His definitive book on the subject written in 300 BCE described and proved most of the facts that students learn today in school. Euclid is known as The Father of Geometry.
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