Abstract
The first topic which I shall discuss will be the numbers e and π. In particular, I wish to prove that they are transcendental numbers.
Interest in the number π, in geometric form, dates from ancient times. Even then it was usual to distinguish between the problem of its approximate calculation and that of its exact theoretical construction; and one had certain approaches for the solution of both problems. Archimedes made an essential advance, in the first, with his process of approximating to the circle by means of inscribed and circumscribed polygons. The second problem soon centred in the question as to whether or not it was possible to construct π with ruler and compass. This was attempted in all possible ways with never a suspicion that the reason for continued failure was the impossibility of the construction. An account of some of the early attempts has been published by Ferdinand Rudio.
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© 2016 Springer-Verlag Berlin Heidelberg
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Klein, F. (2016). IV. Supplement. In: Elementary Mathematics from a Higher Standpoint. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-49442-4_12
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DOI: https://doi.org/10.1007/978-3-662-49442-4_12
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