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].	Astrophysics and Cosmology [Astrophysique et Cosmologie].	Deterministic Chaos [Chaos Déterministe].
Miscellaneous [Divers].

Didactical Pictures [Images didactiques]:

Mathematics [Mathématiques]:

More pictures about Mathematics

$The history of Mathematics$
The history of Mathematics.

An equilateral triangle.

A right-angled triangle.

A demonstration of the Pythagoras' theorem.

Two sets.

A bijection.

To count the members of a set.

A set 'E'.

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

Two sets 'SE1' and 'SE2'.

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

The 20 first digits {1,4,1,5,9,2,6,5,3,5,8,9,7,9,3,2,3,8,4,6} of 'pi' displayed on an helix -orange-.

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).

Generation of the 63 first Conway's surreal numbers.

Generation of the 63x63 first Conway's surreal complex numbers.

The continuity.

The differentiability.

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

The continuity.

The differentiability.

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

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

A point.

A 0-cube -a point-.

A 1-cube -a segment-.

A 2-cube -a square-.

A 3-cube -a cube-.

A 4-cube -an hypercube-.

A 0-cube -a point-.	A 1-cube -a segment-.	A 2-cube -a square-.	A 3-cube -a cube-.	A 4-cube -an hypercube-.
A distorded -for the sake of display- 5-cube -an hyperhypercube-.

The Golden Rectangle.

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

The two subdivisions of the 'flat' Golden Triangle.

The 'flat' Golden Triangle.

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

The two subdivisions of the 'sharp' Golden Triangle.

The 'sharp' Golden Triangle.

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

The parallel axiom of the Euclidian Geometry.

A plane -zero curvature-.

The Spherical Geometry.

An hexagonal tiling of the hyperbolic Poincaré disk -iteration 5-.

A one sheet hyperboloid of revolution -negative curvature-.

Tridimensional representation of our familiar tridimensional space.

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

A cylinder -a bidimensional manifold-.

Bidimensional cross-sections of a cylinder.	Bidimensional cross-sections of a cylinder.	Bidimensional cross-sections of the Klein bottle.	Bidimensional cross-sections of the Klein bottle.	Bidimensional cross-sections of the Bonan-Jeener-Klein triple bottle.
Bidimensional cross-sections of the Bonan-Jeener-Klein triple bottle.	Bidimensional cross-sections of the Jeener unilateral node.	Bidimensional cross-sections of the Jeener unilateral node.

To add two numbers.

To multiply two numbers.

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.

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

Fractal Geometry [Géométrie Fractale]:

More pictures about Deterministic Fractal Geometry

More pictures about Non Deterministic Fractal Geometry

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.

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

About the length 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

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

$The self-similarity of a perfect bidimensional fractal tree$
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 Cantor triadic set -iterations 0 to 5-.

The Sierpinski carpet -iteration 1-.	The Sierpinski carpet -iteration 2-.	The Sierpinski carpet -iteration 3-.	The Sierpinski carpet -iteration 4-.	The Sierpinski carpet -iteration 5-.
The construction process of the Sierpinski carpet.

The Menger sponge -iteration 1-.	The Menger sponge -iteration 2-.	The Menger sponge -iteration 3-.	The Menger sponge -iteration 4-.	The Menger sponge -iteration 5-.
The construction process of the Menger sponge.

The Menger sponge -iteration 1-.	The Menger sponge -iteration 2-.	The Menger sponge -iteration 3-.	The Menger sponge -iteration 4-.	The Menger sponge -iteration 5-.
The construction process of the Menger sponge.

Bidimensional Hilbert Curve -iteration 1-.	Bidimensional Hilbert Curve -iteration 2-.	Bidimensional Hilbert Curve -iteration 3-.	Bidimensional Hilbert Curve -iteration 4-.	Bidimensional Hilbert Curve -iteration 5-.
Bidimensional Hilbert Curve -iterations 1 to 5-.