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Topic: Quadrature of lunes
Replies: 2   Last Post: Oct 19, 2011 11:02 AM

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Posts: 1
From: Ljubljana, Slovenia
Registered: 1/4/06
Quadrature of lunes
Posted: Jan 5, 2006 1:38 PM
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Hi, there!

Due to its importance in the history of mathematics there is extensive literature on Hippocrates lunes. However, except for the original papers of Tschebotarow and Dorodnov I was not able to find in the literature a proof of the existence of exactly five squarable lunes. In particular, I am having problems understanding one of the cases in Tschebotarow's original proof (case 4. on page 174 of the paper N. Tschebotarow: Uber quadrierbare Kreisbogenzweiecke I, Mathematische Zeitschrift 39 (1934), pp. 161-175): How to see that the polynomial
x^27 - 1 - sqrt{27/11) x^8 (x^11 - 1)
has no factor of degree some power of 2. Tschebotarew suggests using reductions modulo 3 and modulo 11.

Any help would be greatly appreciated.

Best, Tomaz

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