Lectures On Mathematics Delivered From Aug 28 to Sept 9 1893 Before Members
Lectures On Mathematics Delivered From Aug 28 to Sept 9 1893 Before Members
Klein, Felix, 1849-1925
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Nine years later, Lindemann, f taking the develop- ments of Hermite as his point of departure, succeeded in proving the transcendency of TT. Lindemann's work was verified soon after by Weierstrass. The proof that TT is a transcendental number will forever mark an epoch in mathematical science. It gives the final answer to the problem of squaring the circle and settles this vexed question once for all. This problem requires to derive the number TT by a finite number of elementary geometrical pro...cesses, i. E. With the use of the ruler and compasses alone. As a straight line and a circle, or two circles, have only two intersections, these processes, or any finite combination of them, can be expressed algebraically in a comparatively simple form, so that a solution of the problem of squaring the circle would mean that TT can be expressed as the root of an algebraic equation of a comparatively simple kind, viz. One that is solvable by square roots. Lindemann's proof shows that TT is not the root of any algebraic equation.
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