EP1280587B1 - Elements structuraux et jeux de carreaux - Google Patents

Elements structuraux et jeux de carreaux Download PDF

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Publication number
EP1280587B1
EP1280587B1 EP01938162A EP01938162A EP1280587B1 EP 1280587 B1 EP1280587 B1 EP 1280587B1 EP 01938162 A EP01938162 A EP 01938162A EP 01938162 A EP01938162 A EP 01938162A EP 1280587 B1 EP1280587 B1 EP 1280587B1
Authority
EP
European Patent Office
Prior art keywords
structural elements
lines
ipentas
accordance
fact
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Expired - Lifetime
Application number
EP01938162A
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German (de)
English (en)
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EP1280587A1 (fr
Inventor
Bernhard Geissler
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Individual
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Individual
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Classifications

    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B44—DECORATIVE ARTS
    • B44F—SPECIAL DESIGNS OR PICTURES
    • B44F3/00—Designs characterised by outlines
    • A—HUMAN NECESSITIES
    • A63—SPORTS; GAMES; AMUSEMENTS
    • A63F—CARD, BOARD, OR ROULETTE GAMES; INDOOR GAMES USING SMALL MOVING PLAYING BODIES; VIDEO GAMES; GAMES NOT OTHERWISE PROVIDED FOR
    • A63F9/00—Games not otherwise provided for
    • A63F9/06—Patience; Other games for self-amusement
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B44—DECORATIVE ARTS
    • B44C—PRODUCING DECORATIVE EFFECTS; MOSAICS; TARSIA WORK; PAPERHANGING
    • B44C3/00—Processes, not specifically provided for elsewhere, for producing ornamental structures
    • B44C3/12—Uniting ornamental elements to structures, e.g. mosaic plates
    • B44C3/123—Mosaic constructs
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B44—DECORATIVE ARTS
    • B44F—SPECIAL DESIGNS OR PICTURES
    • B44F11/00—Designs imitating artistic work
    • B44F11/04—Imitation of mosaic or tarsia-work patterns
    • E—FIXED CONSTRUCTIONS
    • E04—BUILDING
    • E04F—FINISHING WORK ON BUILDINGS, e.g. STAIRS, FLOORS
    • E04F15/00—Flooring
    • E04F15/02—Flooring or floor layers composed of a number of similar elements
    • A—HUMAN NECESSITIES
    • A63—SPORTS; GAMES; AMUSEMENTS
    • A63F—CARD, BOARD, OR ROULETTE GAMES; INDOOR GAMES USING SMALL MOVING PLAYING BODIES; VIDEO GAMES; GAMES NOT OTHERWISE PROVIDED FOR
    • A63F9/00—Games not otherwise provided for
    • A63F9/06—Patience; Other games for self-amusement
    • A63F9/0669—Tesselation
    • A63F2009/067—Tesselation using a particular shape of tile
    • A63F2009/0681—Tesselation using a particular shape of tile pentagonal
    • A—HUMAN NECESSITIES
    • A63—SPORTS; GAMES; AMUSEMENTS
    • A63F—CARD, BOARD, OR ROULETTE GAMES; INDOOR GAMES USING SMALL MOVING PLAYING BODIES; VIDEO GAMES; GAMES NOT OTHERWISE PROVIDED FOR
    • A63F9/00—Games not otherwise provided for
    • A63F9/06—Patience; Other games for self-amusement
    • A63F9/0669—Tesselation
    • A63F2009/0695—Tesselation using different types of tiles
    • A—HUMAN NECESSITIES
    • A63—SPORTS; GAMES; AMUSEMENTS
    • A63F—CARD, BOARD, OR ROULETTE GAMES; INDOOR GAMES USING SMALL MOVING PLAYING BODIES; VIDEO GAMES; GAMES NOT OTHERWISE PROVIDED FOR
    • A63F9/00—Games not otherwise provided for
    • A63F9/06—Patience; Other games for self-amusement
    • A63F9/0669—Tesselation
    • A63F2009/0695—Tesselation using different types of tiles
    • A63F2009/0697—Tesselation using different types of tiles of polygonal shapes

Definitions

  • the invention relates to structural elements as well as sets of structural elements or tiles with geometrically defined outlines, which are also referred to below simply as "tiles", as well as surface patterns assembled from such structural elements or tiles.
  • the invention also relates to applications of these sets of structural elements in paving, tiling, puzzles, laying games, marquetry, fabric swatches and jewelery.
  • Numerous puzzles use sets of tiles with geometrically defined structural elements, such as the well-known Tangram or the pentagonal puzzle of the U.S. Patent 4,343,471 , These puzzle geometric puzzles consist of a number of different tiles.
  • the tile sets paving the plane are usually limited in possible structures. For example, pavings made of square or hexagonal tiles can only be displayed in a single periodic structure.
  • parquet or intarsia structures would be of interest to tile sets containing a variety of different structures or patterns in periodic or non-periodic Allow species, but consist of only one or very few different tile types.
  • a set of structural elements or tiles is indicated with geometric outlines, as defined in the claims. All the tiles of this set, which of course may be combined with other sets, consist of or derive from equilateral, non-regular pentagons with interior angles of 36 °, 108 °, 108 °, 36 °, 252 °. These equilateral pentagons are also called "Ipenta (s)" in the following.
  • Sets of congruent ipentas pave the plane in many ways according to the invention, in particular periodically, not periodically, symmetrically and not symmetrically.
  • the paving can i.a. have a decagonal basic structure, a parallelogram structure and various helical structures.
  • each pattern can be represented by tiles of two different colors such that they do not collide along a pentagon side with a tile of the same color. It then results in a quasi-checkered structure.
  • the sets or groups of structural elements according to the invention may in particular also contain modifications of the pentas, as described in more detail below.
  • novel sets of structural elements can preferably be used for the following applications, which in turn represent articles or further embodiments of the invention.
  • the pattern sets may be tile sets for outdoor or indoor use. They can be used to cover floor areas, squares and walls. These tiles can be made of all common materials such as ceramic, marble, gemstones, plastic, metal or wood.
  • the corners may be rounded, preferably with the same radius of curvature in the corners or with a convexly or concavely three times congruent repetitive at the large corners curvature portions of the smaller corner. As a result, the curves fit smoothly in all patterns.
  • the structure sets can be used for laying games, especially for puzzles. These puzzles can be conventionally provided with pictures to be laid. These games or puzzles according to the invention preferably have a fixed predetermined edge region, or they can be cut smoothly, for example, to create a rectangular edge, which then, however, arise from the congruent puzzle pieces edge pieces.
  • the pattern sets can be used for a game in which two or more players alternately put the structural elements together and z. B. wins the player who can lay the last structural element. Since the structural elements can be placed not only in the area located within the edge in fully covering manner, it is not clear from the outset how many Structural elements can be placed. Rather, this depends exclusively on how the structural elements are laid. By alternately laying a structural element or even several (for example, by the number of a cube defined) structural elements to each other on one or more pages, interesting game variants may arise.
  • the inventive games preferably have a greater number of structural elements, in particular more than nine and the structural elements all preferably consist of one or two sets of congruent structural elements, and optionally the above-mentioned frame area.
  • the sides of the pentas, or the structures emerging from them are replaced by lines which lead to their being caught when the puzzle pieces are laid.
  • this can be done by replacing each of the five sides with a line drawn to the left and centrically symmetrically to the right, which makes possible undercuts or entanglements.
  • the sets of structural elements made of wood, stone, ceramic, glass, plastic, metal, or gemstone can be formed into Intarsien Modellen. Despite their geometric rigor, these structures can be formed into different images by multiple matching of the structural elements.
  • the sets of structural elements can be composed into fabric patterns and the like, in which the entire surface is completely or substantially completely covered by pentas or modified pentas, but the contours are not repeated due to randomization or random distribution.
  • the preferred embodiment has a periodically repeating hexagonal subregion of eight Ipentas, in which the Ipentas can, however, be arranged differently distributed from subarea to subarea, so that, despite the periodicity of the edge of the subgroup, a statistical nonperiodic arrangement of the Ipentas results , For most observers, the hexagonal structure of the subregions disappears.
  • Another object of the invention are new structural elements or tiles, which are derived from the Ipentas.
  • a first group of these structural elements results from the pentas by replacing each side of the pentas by a polyline, a vector sequence or a curve section (hereafter 'curve section') in which the distance between the end points is the same, and where at least one is not straightforward.
  • all five curve sections are equal, resulting in one or two new modified ipentas each having five 'major corners' spanning an Ipenta. If the curve sections are centrally symmetrical, only one structural element results at a time. Otherwise, there are two, depending on whether that Replacing the five sides of the pentagon by the curve sections clockwise or counterclockwise takes place.
  • the curve sections have a centrally symmetrical S or Z shape are particularly preferred.
  • the curve sections cause hooking of the juxtaposed structural elements.
  • the latter can be achieved in that at least two partial sections of the curve sections form an angle of more than 180 ° with each other.
  • the curve sections neither intersect nor intersect the curve sections of the other sides of the pentagon.
  • the curve sections consist of two line elements that form an angle of 144 °, there are two structural elements with eight or six corners. With the structural element with six corners, the respective double lines running back and forth are simply left out since they occupy the 'zero' area.
  • the polyline consists of a number of n> 2 sections and the angle between the first and the last section is 144 °, then a paving of Ipentas results in a paving of two groups of congruent tiles, in which the perimeter of the two tiles different from each other. The difference in circumferential lengths is four times the overlap of said first and last portions of the polyline. Again, the overlapping line sections of the smaller feature are omitted.
  • the disclosure also provides new tiles, also derived from Ipentas, having an outline resulting from the fact that at least two Ipentas are juxtaposed along one or two sides.
  • the structural elements are preferably composed of two pentagons placed in such a way, whereby seven different (without reflections) structural elements, six with eight and one with six equal sides arise. Three of these structural elements can pave the plane periodically or not periodically, with only the line-symmetric structural element allowing the paving with this one structural element. The other two structural elements can only pave the plane together with the structural elements which are mirror-symmetrical to them. These three structural elements, two with eight and one with six sides, are preferred in this group. Even with these structural elements, each page can be replaced by a curve section. This results in one or two groups of structural elements, which in the case of paving e.g. can be hooked together.
  • FIG. 2 shows a non-periodic, centrally symmetrical paving of Ipentas 1 and 2. Here, too, adjacent structural elements change color.
  • FIG. 3 shows a non-periodic paving of Ipentas. Eight of these Ipentas (four bright and four dark) form a hexagon. The outlines of these hexagons pave the plane periodically, the ipentas themselves do not periodically pave, and the two possible arrangements of the eight ipentas in the hexagon were determined by a random distribution. Likewise, however, an algorithm can also be used for this purpose.
  • each two structural elements or tiles are shown, which result from Ipentas as follows: First, in the Ipentas each page by two equal long lines forming an angle of 144 ° with each other form, replaced. As a result, as described above, two structural elements 9 and 10 are formed, as shown in FIGS. 11b and c and in a pavement in FIG. 11d. If one then replaces each of these ten or six sides of these structural elements with the corresponding polylines, as has also been done in the corresponding representations of FIGS. 7a-h for the pentas themselves, this results in modified structural elements shown.
  • the structural elements 8a-1 and 8a-2 (and corresponding to 8b-h) together pave the plane, e.g. hooked together.
  • FIGS. 9a-g show the seven structural elements which result when two ipentas are laid together along one side or two sides.
  • Fig. 9h is shown how these seven structural elements can be placed in a closed form with a minimum of circumference. From these structural elements, three structural elements are particularly preferred, since these pave the plane periodically and not periodically, either alone or together with other or the structural elements appearing mirror-symmetrical to them. These are the structural elements gem.
  • Fig. 9a, 9f, 9g As a result, they can also be used for the above-mentioned applications. It is in the structural element gem.
  • Fig. 9g is an equilateral equilateral hexagon resulting from two ipentas placed along two sides. In the case of the structural elements of FIGS. 9a and 9f, they are equilateral irregular octagonal structural elements which have been created by laying two pentas along one side.
  • FIGS. 9f and 9g Non-periodic tiling from the structural elements acc.
  • Figures 9a, 9f, 9g are shown in Figures 5, 6 and 4. Only the structural element gem.
  • Fig. 9a paves the plane alone, see Fig. 5.
  • FIGS. 9f and 9g additionally require the respective mirror-symmetrical structural elements which are represented in FIG. 6 by the gaps between the structural elements (or by white elements).
  • Figs. 10a and b there are shown two patches with modified Ipentas 7 and 8 having a spiral structure, and Fig. 10b comprising the arrangement of Fig. 10a and showing the growing spiral.
  • the individual structural elements 7 and 8 correspond to the structural element shown in FIG. 7d.
  • FIGS. 11a-d show how new structural elements 9 and 10 result from the pentas.
  • the output ppation of pure Ipentas is shown in Fig. 11a. If one replaces each side of this initial paving by a polyline of two lines that enclose an angle of 144 °, then the paving results in accordance with.
  • Fig. 11d wherein the double lines have been omitted as described. This results in two sets of tiles, which are shown individually in Fig. 11b and Fig. 11c.
  • the first set consists of equilateral decagonal structural elements, while the second set consists of equilateral hexagonal structural elements.
  • the decagonal structural element is equilateral and has the angles 288 °, 144 °, 72 °, 144 °, 144 °, 144 °, 144 °, 72 °, 144 °.
  • the hexagonal structural element has the same side length as the decagonal structural element, the angles being 72 °, 72 °, 216 °, 72 °, 72 °, 216 °.
  • Laying games from the above paving preferably have an edge enclosing the paving without touching, e.g. B. on a rectangular edge, which limits the laying game, which may be made of cardboard, plastic or wood, for example, outwards and defines a closed edge region surrounding the interior.
  • the interior is densely filled by the inventive set of structural elements, or by the two sets shown. This makes it possible to realize jigsaw puzzles or other laying games. It also games can be formed so that one side is usable as a puzzle and the other side without figure and with structural elements of the same color or with structural elements of different colors eg up to six colors is formed.
  • the so one-sided play game can play games in many ways, in which one determines the winner after who sets the last element. Or you can use a die to determine how many elements the player has to lay, and to determine the winner or the loser according to the number of structural elements placed or the number of elements that can no longer be laid. It is also possible to set game rules, according to which the goal is to connect two edge sides with a continuous chain of own elements, or to enclose areas defined by a color, thereby making the enclosed areas as large as possible, the size of which being determined by the number of side by side is defined in the enclosed area insertable structural elements. This results in games that are related to the NIM games or the GO, but additionally addresses the understanding of the player for the geometry of the structural elements and thus have a further learning effect.
  • the structural elements are limited in their displaceability by magnetic forces. Also, the structural elements with undercuts that define the abutment against each other and secure against displacement, are useful for this purpose.

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  • Engineering & Computer Science (AREA)
  • Architecture (AREA)
  • Civil Engineering (AREA)
  • Structural Engineering (AREA)
  • Multimedia (AREA)
  • Finishing Walls (AREA)
  • Floor Finish (AREA)
  • Toys (AREA)
  • Adornments (AREA)

Claims (8)

  1. Jeu de pose constitué d'une zone de bord fermée et d'une zone de pose qui est entourée par celle-ci et qui peut être remplie à l'aide d'un groupe d'éléments structurels, ces éléments structurels étant dérivés d'un pentagone équilatéral irrégulier dont les angles sont de 36°, 108°, 108°, 36° et 252° (ipenta), ce groupe étant constitué soit
    a) d'éléments structurels congruents SA dont le périmètre est constitué de cinq lignes LF qui relient de manière fermée les sommets de l'ipenta, les lignes LF étant des lignes à symétrie centrale congruentes entre elles qui ne se coupent pas et, sauf aux sommets de l'ipenta, ne se touchent pas non plus,
    soit
    b) de deux sous-groupes d'éléments structurels dans lesquels les sommets de l'ipenta sont reliés par des lignes congruentes entre elles LF comportant chacune deux portions d'égale longueur LZ qui forment un angle de 144°, à savoir
    aa) un sous-groupe UA d'éléments structurels congruents SA qui forment un décagone équilatéral irrégulier avec les angles intérieurs 288°, 144°, 72°, 144°, 144°, 144°, 144°, 144°, 72°, 144° et
    bb) un sous-groupe supplémentaire UB d'environ autant de seconds éléments structurels SB qui forment un hexagone équilatéral irrégulier avec six éléments linéaires LS de même longueur de côté que LZ et avec des angles intérieurs de 72°, 216°, 72°, 72°, 216°, 72°.
  2. Jeu de pose selon la revendication 1, caractérisé en ce qu'il comporte une ou plusieurs sous-zones reposant sur huit ipentas qui forment un hexagone.
  3. Jeu de pose selon la revendication 1 ou 2, caractérisé en ce que les portions LS, respectivement LZ des éléments structurels des sous-groupes UA et UB sont remplacées par des lignes congruentes, à symétrie centrale, non droites.
  4. Jeu de pose selon une des revendications 1 à 3, caractérisé en ce que les lignes à symétrie centrale ne se coupent pas et forment des lignes arrondies.
  5. Jeu de pose selon la revendication 3, caractérisé en ce que les lignes à symétrie centrale comportent des contre-dépouilles pour l'accrochage mutuel des éléments structurels.
  6. Jeu de pose selon une des revendications 1 à 5, caractérisé en ce que les éléments structurels sont des éléments de puzzle.
  7. Jeu de pose selon une des revendications 1 à 6, caractérisé en ce que les éléments structurels ont des surfaces différentes.
  8. Jeu de pose selon une des revendications 1 à 7, caractérisé en ce que les éléments structurels présentent des sommets arrondis.
EP01938162A 2000-05-04 2001-05-04 Elements structuraux et jeux de carreaux Expired - Lifetime EP1280587B1 (fr)

Applications Claiming Priority (3)

Application Number Priority Date Filing Date Title
DE10021607 2000-05-04
DE10021607 2000-05-04
PCT/EP2001/005058 WO2001085274A1 (fr) 2000-05-04 2001-05-04 Elements structuraux et jeux de carreaux

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EP1280587A1 EP1280587A1 (fr) 2003-02-05
EP1280587B1 true EP1280587B1 (fr) 2007-11-14

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US (2) US20030136069A1 (fr)
EP (1) EP1280587B1 (fr)
JP (1) JP4703933B2 (fr)
CN (1) CN1220537C (fr)
AT (1) ATE378097T1 (fr)
DE (1) DE50113267D1 (fr)
WO (1) WO2001085274A1 (fr)

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Also Published As

Publication number Publication date
WO2001085274A1 (fr) 2001-11-15
JP4703933B2 (ja) 2011-06-15
JP2003532507A (ja) 2003-11-05
DE50113267D1 (de) 2007-12-27
CN1427735A (zh) 2003-07-02
EP1280587A1 (fr) 2003-02-05
US20030136069A1 (en) 2003-07-24
US7284757B2 (en) 2007-10-23
US20070069463A1 (en) 2007-03-29
ATE378097T1 (de) 2007-11-15
CN1220537C (zh) 2005-09-28

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