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

Voir

Publié par

pefav

Nombre de lectures

Langue

English

Poids de l'ouvrage

1 Mo

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

Voir