Abstract
In this paper, we prove the existence of the Poncelet-Morley point for a given elliptic configuration. The paper ends with an application of such a point in angle trisection problem.
Highlights
Trisection is a classic problem of compass and straightedge constructions of ancient Greek mathematics
We prove the existence of the Poncelet-Morley point for a given elliptic configuration
The paper ends with an application of such a point in angle trisection problem
Summary
Trisection is a classic problem of compass and straightedge constructions of ancient Greek mathematics. Note that the fact that there is no way to trisect an angle in general with just a compass and a straightedge does not mean that there is no trisecting angle: for example, it is relatively straightforward to trisect a right angle, that is, to construct an angle of measure 30 degrees It is, possible to trisect an arbitrary angle by using tools other than straightedge and compass. We need the Poncelet result to prove the existence of our main tool called the Poncelet-Morley point for a given configuration. We recall that it was in 1813 during his captivity as war prisoner that J. We use the Poncelet-Morley point to prove that it is not possible to trisect all angles
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