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Fiche 1,  Justifications,  Anglais

Record number: 1, Textual support number: 1 DEF

The residual set of an Apollonian packing.  2, fiche 1, Anglais, - Apollonian%20gasket

Record number: 1, Textual support number: 1 CONT

The Apollonian construction concludes with five circles, three given and two Apollonian, which together define six circular triangles. Repeating the same procedure, we draw the largest inscribed circle in each triangle. Infinite further repetition is called Apollonian packing. To the resulting infinite collection of circles one adds its limit points, and one obtains a set I call Apollonian net. A portion of net within a circular triangle... is to be called Apollonian gasket.  3, fiche 1, Anglais, - Apollonian%20gasket

Record number: 1, Textual support number: 2 CONT

Formation of an Apollonian gasket : the points that are never inside any of the circles form a set of zero area which is, as it were, more than a line, but less than a surface. Its fractal dimension therefore lies between 1 and 2, though its exact value is not known. It is approximately 1.3.  4, fiche 1, Anglais, - Apollonian%20gasket

Record number: 1, Textual support number: 1 OBS

See Sierpinski gasket.  5, fiche 1, Anglais, - Apollonian%20gasket

Fiche 1,  Justifications,  Français

Record number: 1, Textual support number: 1 DEF

L'ensemble non dénombrable des points à surface nulle qui restent non couverts par un bourrage apollonien.  2, fiche 1, Français, - tamis%20apollonien

Record number: 1, Textual support number: 1 OBS

Voir bourrage, entassement.  3, fiche 1, Français, - tamis%20apollonien

Fiche 1,  Justifications,  Espagnol

Fiche 2,  Justifications,  Anglais

Record number: 2, Textual support number: 1 DEF

Packing obtained when a sequence of closed balls V is the interior of a curvilinear triangle in a bidimensional space. Different from "osculatory packing".  2, fiche 2, Anglais, - Apollonian%20packing

Record number: 2, Textual support number: 1 CONT

The Apollonian construction concludes with five circles, three given and two Apollonian, which together define six circular triangles. Repeating the same procedure, we draw the largest inscribed circle in each triangle. Infinite further repetition is called Apollonian packing.  3, fiche 2, Anglais, - Apollonian%20packing

Record number: 2, Textual support number: 1 OBS

See Apollonian gasket, packing, worm problem.  4, fiche 2, Anglais, - Apollonian%20packing

Fiche 2,  Justifications,  Français

Record number: 2, Textual support number: 1 DEF

Bourrage obtenu d'un triangle formé de trois boules tangentes deux à deux, par itération infinie de la construction d'Apollonius de Perge (cercles tangents à trois cercles donnés). L'union des intérieurs des cercles couvre presque entièrement le triangle.  3, fiche 2, Français, - bourrage%20apollonien

Record number: 2, Textual support number: 1 OBS

L'ensemble des points non couverts a une surface nulle et constitue un "tamis apollonien".  3, fiche 2, Français, - bourrage%20apollonien

Record number: 2, Textual support number: 2 OBS

Voir bourrage, tamis, tapis de Sierpinski.  4, fiche 2, Français, - bourrage%20apollonien

Fiche 2,  Justifications,  Espagnol

Fiche 3,  Justifications,  Anglais

Record number: 3, Textual support number: 1 DEF

A family of sets in the plane which has no overlaps. ...  2, fiche 3, Anglais, - packing

Record number: 3, Textual support number: 1 OBS

Different aspects of packing are involved in solving the Kakeya (1917) problem (finding the area of the smallest convex set inside which a unit segment can be reversed), the Mastrand (1979) problem (what(are) the minimal comfortable living quarters for a unit worm?), and Cummingham’s bird (1976).  3, fiche 3, Anglais, - packing

Record number: 3, Textual support number: 2 OBS

See gasket, worm problem, Apollonian packing.  3, fiche 3, Anglais, - packing

Record number: 3, Textual support number: 1 PHR

Osculatory packing, curve packing, curved-arcs packing, packings sphere.  4, fiche 3, Anglais, - packing

Fiche 3,  Justifications,  Français

Record number: 3, Textual support number: 1 DEF

Empilement de boules, deux à deux disjointes, qui couvre, ou remplit, une partie d'un espace métrique.  4, fiche 3, Français, - bourrage

Record number: 3, Textual support number: 1 OBS

Concept intégré à la solution du problème de Kakeya (1917), du problème de Besicovitch-Rado (1968), du problème de Mastrand (1979) et du problème "oiseau de Cummingham (1976). La dimension d'entassement (Claude Tricot) combine la capacité de Kolmogorov et la dimension de Hausdorff. Le néologisme "bourrage" est proposé par B. Mandelbrot.  4, fiche 3, Français, - bourrage

Fiche 3,  Justifications,  Espagnol