Wikipedia:Reference desk/Archives/Mathematics/2007 February 25

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February 25

Lindemann-Weierstrass Theorem

Is it possible to prove the Lindemann-Weierstrass Theorem without knowledge of the Fundamental Theorem of Algebra? Every proof I've seen usually has the statement (usually implicitly) that an integral polynomial of degree n has n complex roots.

Triangle

(Sorry I can't speak English as well.) I got a isosceles triangle with the corners ABC. At the side AC is a dot with the name X and at the side BC is a dot with the name Y. The length of AX is the same as BY. Now I must draw two circles, the first goes to the points A, Y and C and the second goes to B, X and C. Now I get another vertex (I hope that vertex is the right name) instead of in the corner C. When I draw now a line between the new vertex and the corner C, I will get a bisection of the angle ACB. Why will I get a bisection?

Think symmetry. Display the triangle with AB horizontal. The two circles are mirror images in a vertical line through C. --KSmrq^T 01:14, 26 February 2007 (UTC)

Sorry but no. I don't have the answer but it's not as simple as that. If it were an equilateral triangle then maybe, but in an isosceles the only symmetry is through point A. One of the circles has AC as a chord and intersects point y, the other has BC as a chord and intersects point x. AC is equal to AB but not to BC. Vespine 02:44, 26 February 2007 (UTC)

You added the assumption that the symmetry is through A; the problem statement did not, and so I assumed C. When you have a proof, get back to us. --KSmrq^T 17:45, 26 February 2007 (UTC)