Gallery:

Didactical Pictures

[Galerie: Images didactiques]

Jean-François COLONNA

www.lactamme.polytechnique.fr

jean-francois.colonna@polytechnique.edu
CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641, Ecole Polytechnique, CNRS, 91128 Palaiseau Cedex, France

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Didactical Pictures [Images didactiques]:

Mathematics
[Mathématiques].

Fractal Geometry
[Géométrie Fractale].

Celestial Mechanics
[Mécanique Céleste].

Miscellaneous
[Divers].

Didactical Pictures [Images didactiques]:

Mathematics [Mathématiques]:

A demonstration of the Pythagoras' theorem

A demonstration of the Pythagoras' theorem.

A bijection

A bijection

A set 'E'

Two subsets 'SE1' and 'SE2' of a set 'E'

Two subsets 'SE1' and 'SE2' of a set 'E'.

Two sets 'SE1' and 'SE2'

Two sets 'SE1' and 'SE2'.

A set 'F' with two elements 'SE1' and 'SE2'

A set 'F' with two elements 'SE1' and 'SE2'.

The four first power sets {P(E),P(P(E)),P(P(P(E))),P(P(P(P(E))))} of a one-element set E

The four first power sets {P(E),P(P(E)),P(P(P(E))),P(P(P(P(E))))} of a one-element set E.

The Continuum Hypothesis (CH)

The Continuum Hypothesis (CH).

Bidimensional localization of a point P its distances to the three vertices of a triangle ABC being known, the four points being coplanar

Bidimensional localization of a point P its distances to the three vertices of a triangle ABC being known, the four points being coplanar.

Tridimensional localization of a point P its distances to the four vertices of a tetrahedron ABCD being known

Tridimensional localization of a point P its distances to the four vertices of a tetrahedron ABCD being known.

Generation of the 63 first Conway's surreal numbers

Generation of the 63 first Conway's surreal numbers.

Generation of the 2x63-1 first Conway's surreal complex numbers

Generation of the 2x63-1 first Conway's surreal complex numbers.

The continuity

The continuity.

The differentiability

The differentiability.

Definition of a tangent -orange- by means of a secant -red-

Definition of a tangent -orange- by means of a secant -red-.

The continuity

The continuity.

The differentiability

The differentiability.

Definition of a tangent -yellow- by means of a secant -orange-

Definition of a tangent -yellow- by means of a secant -orange-.

The volume of a cube K -U being the unity cube-

The volume of a cube K -U being the unity cube-.

A 4-cube -an hypercube-

A 4-cube -an hypercube-.

The Golden Rectangle

The Golden Rectangle.

Recursive subdivision of the Golden Rectangle by means of the Golden Ratio -phi-

Recursive subdivision of the Golden Rectangle by means of the Golden Ratio -phi-.

The two subdivisions of the 'flat' Golden Triangle

The two subdivisions of the 'flat' Golden Triangle.

The 'flat' Golden Triangle

The 'flat' Golden Triangle.

One of the two subdivisions of the 'flat' Golden Triangle

One of the two subdivisions of the 'flat' Golden Triangle.

One of the two subdivisions of the 'flat' Golden Triangle

One of the two subdivisions of the 'flat' Golden Triangle.

The two subdivisions of the 'sharp' Golden Triangle

The two subdivisions of the 'sharp' Golden Triangle.

The 'sharp' Golden Triangle

The 'sharp' Golden Triangle.

One of the two subdivisions of the 'sharp' Golden Triangle

One of the two subdivisions of the 'sharp' Golden Triangle.

One of the two subdivisions of the 'sharp' Golden Triangle

One of the two subdivisions of the 'sharp' Golden Triangle.

A straigth line -a monodimensional manifold- or a cylinder -a bidimensional manifold- in the distance?

A straigth line -a monodimensional manifold- or a cylinder -a bidimensional manifold- in the distance?.

A cylinder -a bidimensional manifold-

A cylinder -a bidimensional manifold-.

A cylinder -a bidimensional manifold-

A cylinder -a bidimensional manifold-.

To add two numbers

To add two numbers.

To multiply two numbers

To multiply two numbers.

The abelian -commutative- group defined on elliptic curves

The abelian -commutative- group defined on elliptic curves.

Bidimensional localization of a point P its distances to the three vertices of a triangle ABC being known, the four points being coplanar

Bidimensional localization of a point P its distances to the three vertices of a triangle ABC being known, the four points being coplanar.

Tridimensional localization of a point P its distances to the four vertices of a tetrahedron ABCD being known

Tridimensional localization of a point P its distances to the four vertices of a tetrahedron ABCD being known.

Fractal Geometry [Géométrie Fractale]:

The construction process of the von Koch curve -the starting point: a segment-.	The construction process of the von Koch curve -iteration 1: an equilateral triangle-.	The construction process of the von Koch curve -iteration 1: the removing of the base of the equilateral triangle-.	The construction process of the von Koch curve -iteration 2: four equilateral triangles-.	The construction process of the von Koch curve -iteration 2: the removing of the bases of the four equilateral triangles-.
The construction process of the von Koch curve -iteration 3-.	The construction process of the von Koch curve -iteration 3-.	The first two iterations of the construction of the von Koch curve.	The construction of the von Koch curve.	The construction process of the von Koch curve.

About the length of the von Koch curve

About the length of the von Koch curve.

About the length of the von Koch curve

About the length of the von Koch curve.

About the length of the von Koch curve

About the length of the von Koch curve.

About the length of the von Koch curve

About the length of the von Koch curve.

The length of the first two iterations of the construction of the von Koch curve

The length of the first two iterations of the construction of the von Koch curve.

The self-similarity of the von Koch curve

The self-similarity of the von Koch curve.

The self-similarity of the von Koch curve displayed by means of a zoom in with a ratio that is equal to 3

The self-similarity of the von Koch curve displayed by means of a zoom in with a ratio that is equal to 3.

$About the fractal dimension with the first two iterations -red and green respectively- of the construction of the von Koch curve$
About the fractal dimension with the first two iterations -red and green respectively- of the construction of the von Koch curve.

$About the fractal dimension with the first two iterations -red and magenta respectively- of the construction of the von Koch curve$
About the fractal dimension with the first two iterations -red and magenta respectively- of the construction of the von Koch curve.

$A perfect bidimensional fractal tree and the self-similarity$
A perfect bidimensional fractal tree and the self-similarity.

$A perfect bidimensional fractal tree and the self-similarity$
A perfect bidimensional fractal tree and the self-similarity.

$The self-similarity of a perfect bidimensional fractal tree$
The self-similarity of a perfect bidimensional fractal tree.

$A random bidimensional fractal tree and the self-similarity$
A random bidimensional fractal tree and the self-similarity.

$The self-similarity of a random bidimensional fractal tree$
The self-similarity of a random bidimensional fractal tree.

The Sierpinski carpet -iteration 1-

The Sierpinski carpet -iteration 1-.

The Sierpinski carpet -iteration 2-

The Sierpinski carpet -iteration 2-.

The construction process of the Sierpinski carpet

The construction process of the Sierpinski carpet.

The Menger sponge -iteration 1-

The Menger sponge -iteration 1-.

The Menger sponge -iteration 2-

The Menger sponge -iteration 2-.

The construction process of the Menger sponge

The construction process of the Menger sponge.

The Menger sponge -iteration 1-

The Menger sponge -iteration 1-.

The Menger sponge -iteration 2-

The Menger sponge -iteration 2-.

The construction process of the Menger sponge

The construction process of the Menger sponge.

Bidimensional Hilbert Curve -iterations 1 to 5-

Bidimensional Hilbert Curve -iterations 1 to 5-.

Tridimensional Hilbert Curve -iterations 1 to 3-

Tridimensional Hilbert Curve -iterations 1 to 3-.

The Mandelbrot set

The Mandelbrot set.

Iterations in the complex plane

Iterations in the complex plane.

Iterations in the complex plane: the computation of the Mandelbrot set

Iterations in the complex plane: the computation of the Mandelbrot set.

A Douady rabbit -a complex Julia set computed with A=(-0.13,+0.77)-

A Douady rabbit -a complex Julia set computed with A=(-0.13,+0.77)-.

Iterations in the complex plane: the computation of a Julia set

Iterations in the complex plane: the computation of a Julia set.

Along the border of the Mandelbrot set

Along the border of the Mandelbrot set.

$The iterative process used to generate bidimensional fractal fields (large mesh)$
The iterative process used to generate bidimensional fractal fields (large mesh).

Fractal diffusion front in a bidimensional medium obtained by means of a random walk process

Fractal diffusion front in a bidimensional medium obtained by means of a random walk process.

Celestial Mechanics [Mécanique Céleste]:

The Ptolemaic system with a small light grey circle -the epicycle- whose center describes a larger dark grey circle -the deferend- centered on the Earth -blue sphere-

The Ptolemaic system with a small light grey circle -the epicycle- whose center describes a larger dark grey circle -the deferend- centered on the Earth -blue sphere-.

The Ptolemaic system with a small light grey circle -the epicycle- whose center describes a larger dark grey circle -the deferend- centered on the Earth -blue sphere-

The Ptolemaic system with a small light grey circle -the epicycle- whose center describes a larger dark grey circle -the deferend- centered on the Earth -blue sphere-.

Miscellaneous [Divers]:

Free fall in the vacuum

Free fall in the vacuum.

The rain (or the snow)is falling

The rain (or the snow) is falling.

A childish Sun

A childish Sun.

The RGB cube and the additive synthesis of colors

The RGB cube and the additive synthesis of colors.

Anaglyphic glasses

Anaglyphic glasses.

The 'Tapestry' effect applied to a right-angled triangle

The 'Tapestry' effect applied to a right-angled triangle.

The 'CenterOf' effect applied to a right-angled triangle

The 'CenterOf' effect applied to a right-angled triangle.

Copyright (c) Jean-François Colonna, 2016-2019.
Copyright (c) CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / Ecole Polytechnique, 2016-2019.