About this book
Contents
Dossier 1: π , the king of numbers
It is undoubtedly the most famous constant in all of mathematics after 0 or 1. The number π, whose history spans several millennia and continues to be written to this day, exerts a manifest fascination
Topics covered
It's a whole story It is everywhere! A number that defies reason The infinite quest for decimals The number π, quite a poem Squaring the circle: new progress! π-thèque
Dossier 2: The transcendent friends
The emergence of the notion of irrationality, with the impossibility for certain numbers to be written as a quotient of integers, was a highlight of mathematics. When they are not solutions to a polynomial equation with integer coefficients, they are called transcendental.
Topics covered
You said "transcendental"? On the road to transcendence Liouville numbers At the heart of transcendental numbers A story of e The Dottie number or the secrets of cosine To be, or not to be...
Dossier 3: The algebraic family
In the universe of real numbers, one is transcendental or algebraic. This is the case, for example, of all constructible numbers with a ruler and compass. A specificity of the set of algebraic numbers is that it possesses a field structure.
Topics covered
New numbers with Richard Dedekind The radical problem The first irrationals What material are numbers made of? The spirit of quadratic fields When algebra meets geometry
Dossier 4: Irrational curiosities
Non-fractional quantities, such as π or √2, led to questions about the concept of number. It is undoubtedly thanks to decimal notation that the notion of irrational number could be better understood. But from there to proving that a specific number is one, there is a big step!
Topics covered
Numbers or not? Writing the reals Irrationals in the courtyard sine and cosine: rational or not? Decimal development of the sonnet Philippe Leblanc, an artist who plays with numbers
Dossier 5: Numbers from elsewhere
Since any real number can be associated with a decimal expansion, many questions arise about these decimals. New families of numbers have been defined from this, such as normal numbers or universal numbers. Topics covered Everything is normal... or almost! In search of Omega and computable reals Mind-blowing surreal numbers The periods: new numbers
Dossier 1: π , the king of numbers
It is undoubtedly the most famous constant in all of mathematics after 0 or 1. The number π, whose history spans several millennia and continues to be written to this day, exerts a manifest fascination
Topics covered
It's a whole story It is everywhere! A number that defies reason The infinite quest for decimals The number π, quite a poem Squaring the circle: new progress! π-thèque
Dossier 2: The transcendent friends
The emergence of the notion of irrationality, with the impossibility for certain numbers to be written as a quotient of integers, was a highlight of mathematics. When they are not solutions to a polynomial equation with integer coefficients, they are called transcendental.
Topics covered
You said "transcendental"? On the road to transcendence Liouville numbers At the heart of transcendental numbers A story of e The Dottie number or the secrets of cosine To be, or not to be...
Dossier 3: The algebraic family
In the universe of real numbers, one is transcendental or algebraic. This is the case, for example, of all constructible numbers with a ruler and compass. A specificity of the set of algebraic numbers is that it possesses a field structure.
Topics covered
New numbers with Richard Dedekind The radical problem The first irrationals What material are numbers made of? The spirit of quadratic fields When algebra meets geometry
Dossier 4: Irrational curiosities
Non-fractional quantities, such as π or √2, led to questions about the concept of number. It is undoubtedly thanks to decimal notation that the notion of irrational number could be better understood. But from there to proving that a specific number is one, there is a big step!
Topics covered
Numbers or not? Writing the reals Irrationals in the courtyard sine and cosine: rational or not? Decimal development of the sonnet Philippe Leblanc, an artist who plays with numbers
Dossier 5: Numbers from elsewhere
Since any real number can be associated with a decimal expansion, many questions arise about these decimals. New families of numbers have been defined from this, such as normal numbers or universal numbers. Topics covered Everything is normal... or almost! In search of Omega and computable reals Mind-blowing surreal numbers The periods: new numbers