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Geometric constructions in relation with algebraic and transcendental numbers

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Geometric constructions in relation with algebraic and transcendental numbers Jean-Pierre Demailly Academie des Sciences de Paris, and Institut Fourier, Universite de Grenoble I, France February 26, 2010 / Euromath 2010 / Bad Goisern, Austria Jean-Pierre Demailly (Grenoble I), 26/02/2010 Geometric constructions & algebraic numbers

  • bad goisern

  • ancient greek

  • algebraic numbers

  • construction can

  • academie des sciences de paris

  • geometric constructions


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Geometric algebraic
February
c a
onstructions in relation nd transcendental numb
with ers
Jean-Pierre
Demailly
Acad´emiedesSciencesdeParis,and InstitutFourier,Universit´edeGrenobleI,France
26, 2010 / Euromath 2010 /
Jean-Pierre Demailly (Grenoble I), 26/02/2010
Bad Goisern,
Austria
Geometric constructions & algebraic numbers
Ruler and
compasses vs.
origamis
Ancient Greek mathematicians have greatly developed geometry (Euclid, Pythagoras, Thales, Eratosthenes...)
Jean-Pierre Demailly (Grenoble I), 26/02/2010
Geometric constructions & algebraic numbers
Ruler and compasses vs.
origamis
Ancient Greek mathematicians have greatly developed geometry (Euclid, Pythagoras, Thales, Eratosthenes...)
They raised the question whether certain constructions can be made byruler and compasses
Jean-Pierre Demailly (Grenoble I), 26/02/2010
Geometric constructions & algebraic numbers
Ruler and compasses vs. origamis
Ancient Greek mathematicians have greatly developed geometry (Euclid, Pythagoras, Thales, Eratosthenes...)
They raised the question whether certain constructions can be made byruler and compasses Quadrature of the circle ? a square constructingThis means: whose perimeter is equal to the perimeter of a given circle. It was solved only in 1882 by Lindemann, after more than 2000 years : constructionis not possible with ruler and compasses !
Jean-Pierre Demailly (Grenoble I), 26/02/2010
Geometric constructions & algebraic numbers
Ruler and compasses vs.
origamis
Ancient Greek mathematicians have greatly developed geometry (Euclid, Pythagoras, Thales, Eratosthenes...)
They raised the question whether certain constructions can be made byruler and compasses Quadrature of the circle ?This means: a square constructing whose perimeter is equal to the perimeter of a given circle. It was solved only in 1882 by Lindemann, after more than 2000 years : constructionis not possible with ruler and compasses !
Neither is it possible totrisect an angle(Wantzel 1837)
Jean-Pierre Demailly (Grenoble I), 26/02/2010
Geometric constructions & algebraic numbers
Ruler and compasses vs. origamis
Ancient Greek mathematicians have greatly developed geometry (Euclid, Pythagoras, Thales, Eratosthenes...)
They raised the question whether certain constructions can be made byruler and compasses Quadrature of the circle ? a squareThis means: constructing whose perimeter is equal to the perimeter of a given circle. It was solved only in 1882 by Lindemann, after more than 2000 years : constructionis not possible with ruler and compasses !
Neither is it possible totrisect an angle(Wantzel 1837) In Japan, on the other hand, there is a rich tradition of makingorigamis: it is the art offolding paperand maker nice geometric constructions out of such foldings.
Jean-Pierre Demailly (Grenoble I), 26/02/2010
Geometric constructions & algebraic numbers
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