EP0018636B1 - Mosaikelementsatz - Google Patents

Mosaikelementsatz Download PDF

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Publication number
EP0018636B1
EP0018636B1 EP80102350A EP80102350A EP0018636B1 EP 0018636 B1 EP0018636 B1 EP 0018636B1 EP 80102350 A EP80102350 A EP 80102350A EP 80102350 A EP80102350 A EP 80102350A EP 0018636 B1 EP0018636 B1 EP 0018636B1
Authority
EP
European Patent Office
Prior art keywords
mosaic
rhombus
elements
rhombuses
mosaic elements
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
Application number
EP80102350A
Other languages
German (de)
English (en)
French (fr)
Other versions
EP0018636A1 (de
Inventor
Alan H. Schoen
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Individual
Original Assignee
Individual
Priority date (The priority date 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 date listed.)
Filing date
Publication date
Application filed by Individual filed Critical Individual
Priority to AT80102350T priority Critical patent/ATE3695T1/de
Publication of EP0018636A1 publication Critical patent/EP0018636A1/de
Application granted granted Critical
Publication of EP0018636B1 publication Critical patent/EP0018636B1/de
Expired legal-status Critical Current

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Classifications

    • 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
    • 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
    • A63F9/10—Two-dimensional jig-saw puzzles
    • 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
    • A63F9/0669—Tesselation
    • A63F2009/0695—Tesselation using different types of tiles
    • A63F2009/0697—Tesselation using different types of tiles of polygonal shapes
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
    • Y10T—TECHNICAL SUBJECTS COVERED BY FORMER US CLASSIFICATION
    • Y10T428/00—Stock material or miscellaneous articles
    • Y10T428/16—Two dimensionally sectional layer
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
    • Y10T—TECHNICAL SUBJECTS COVERED BY FORMER US CLASSIFICATION
    • Y10T428/00—Stock material or miscellaneous articles
    • Y10T428/16—Two dimensionally sectional layer
    • Y10T428/163—Next to unitary web or sheet of equal or greater extent
    • Y10T428/168—Nonrectangular

Definitions

  • the present invention relates to a mosaic element set of mutually different, polygonal mosaic elements for filling an area which is delimited by a regular polygon with an even number of pages 2n and for forming a basic shape for filling the Euclidean plane, where n means a natural number, the regular polygon can be broken down into a set of (n-1) n / 2 rhombuses and the set of rhombuses consists of a number of real subsets, each of which contains rhombuses of the same shape, but different from subsets to subsets.
  • Mosaic element sets made of mosaic elements or «mosaic stones» can be used for a wide variety of purposes, e.g. B. for street or floor paving, wall or floor tiles, also for games and for illustrative or educational purposes. In practice, the mosaic elements can therefore consist of a wide variety of materials.
  • the most well-known type of mosaic element set is probably the assembly game known as a puzzle, in which an area of very simple shape, e.g. B. a rectangle or circle, is designed with a variety of small pieces of cardboard with irregular and mostly different shapes.
  • An essential peculiarity of such a puzzle is that it can only be assembled in one way.
  • Newer assembly games contain similar pieces with which a variety of shapes can be formed, e.g. B. the so-called «polynominos».
  • composition game from a set of mosaic elements is e.g. B. from US-A-4, 133, 152 (Penrose) known.
  • US-A-3, 065, 970 is a combination game consisting of a set of 29 different "Pentacubes" and an additional Pentacube, which is identical to one of the 29 others, and can be assembled into four different cuboids, all of which Have a volume of 150 unit cubes.
  • the invention as characterized in the claims, creates a mosaic element set consisting of pairs of different mosaic elements, which are able to form the same regular polygon with an even number of sides in the most varied arrangements and also to form a basic shape for filling the Euclidean plane own.
  • the mosaic patterns that can be formed with the mosaic element set according to the invention are very diverse, which can have both aesthetic and practical advantages.
  • the mosaic element set according to the invention is simple to construct, the number of different arrangements that form the regular polygon increases rapidly with an increasing number of pages.
  • the invention can be used to form a hierarchy of composition games with very different levels of difficulty.
  • the mosaic element sets according to the invention can be used for a variety of purposes, e.g. B. as a game, for learning purposes, for test purposes, for tiles, plasters, parquet and. a. m.
  • a regular polygon with an even number of sides 2n is assumed, where n is a natural number.
  • This polygon is divided into rhombic partial areas in a known manner. This gives you a lot of diamonds, but not all of them are different.
  • the next step in determining the configuration of the mosaic elements of the set of mosaic elements according to the invention is now to select exactly one specimen of each type of rhombus from the set of rhombuses. These diamonds form a subset of the set of mosaic elements in the set of mosaic elements.
  • the remaining mosaic elements of the set of mosaic stones of the mosaic element set according to the invention are then formed by pairing the remaining rhombuses according to certain rules. This could also be achieved by using the selected rhombuses, which are different in pairs, as models for additional rhombuses and thus creating an ample supply of rhombuses for pairing.
  • the same amount of mosaic elements can also be used to form a closed surface which forms a basic shape for filling out the Euclidean plane.
  • This is a very remarkable property of the mosaic element set according to the invention, since the basic shape thus formed is not the regular polygon from which the mosaic element set was formed in only two cases.
  • the resulting simple design or covering of a surface is very useful for the production of parquet, tile and wallpaper patterns u. ⁇ .
  • a plurality of mosaic element sets according to the invention can not only be combined to form a corresponding plurality of regular polygons but also to such a polygon and one or more nested rings surrounding it.
  • a regular polygon from a set of mosaic elements according to the invention can be surrounded with three additional sets of mosaic elements so that a further, larger regular polygon is created, this in turn can be surrounded with five additional sets of mosaic elements, so that a further, even larger polygon is created, etc.
  • the mosaic element sets according to the invention also have many other interesting and useful properties.
  • FIG. 1 shows a set of mosaic elements or “mosaic stones” designed according to the invention, which are assembled into a regular polygon with 16 sides.
  • the mosaic elements are different in pairs.
  • the polygon shown can be assembled in a variety of ways using the mosaic element set. 1, more than 200 different arrangements of the mosaic elements are possible.
  • Each of the mosaic elements of the set shown in Figure 1 consists of one or two rhombuses. If one of the mosaic elements is formed from two rhombuses, then there are no collinear edges at any intersection. This allows each intersection at which two diamonds meet, i.e. H. Each joint between the ends of two sides of different rhombuses can be easily recognized by the resulting mosaic element, since the mosaic element has an angle or a corner there. It is therefore obvious that the mosaic elements 1, 2, 3 and 4 each consist of a single rhombus and the remaining mosaic elements each of a pair of rhombuses.
  • the mosaic elements 5, 6 and 7 consist of a square (a special rhombus shape) and another rhombus
  • the mosaic elements 8, 9 and 10 are formed from two identical rhombuses
  • the remaining mosaic elements 11, 12, 13, 14, 15 and 16 is composed of two different rhombuses.
  • the mosaic elements 11 and 15, 12 and 13, 14 and 16 can be called "dizygotic twins" because the rhombuses of each of these pairs match the rhombuses of the other pair, but the different arrangement of the rhombuses of the pairs results in two different mosaic elements.
  • a set of mosaic stones according to the invention can be constructed from each regular polygon with an even number of pages as follows:
  • the regular polygon with an even number of pages is first divided into a set of rhombuses, as shown, for example, in FIG.
  • the four sides of each rhombus are of course each as long as one side of the regular polygon. If the number p of the sides of the polygon is 4q, where q is an arbitrary natural number, the resulting set of rhombuses contains q different types of rhombuses with q squares and 2q rhombuses from each of the other (q-1) types. The total number of rhombuses is therefore q (2q-1). If one now forms the set of mosaic elements according to the invention, q 2 mosaic elements are obtained.
  • Each rhombus type can be uniquely determined by the acute angle, the acute angle must be an integer multiple of 360 ° / p, the integer being no greater than q.
  • the set of rhombuses from which the mosaic elements according to FIG. 1 are formed is shown in FIG. 2.
  • the squares are numbered 4, 5a, 6a and 7a.
  • the four squares therefore result because p is 16 for the polygon shown in FIG. 2 and therefore q must be 4.
  • the square is the extreme case in which the “acute” angle in the rhombus is 90 °.
  • 90 ° is also an integral multiple, namely four times (q times) 360 ° / p.
  • Mosaic elements are now formed from the remaining rhombuses by assembling each of these rhombuses with a rhombus of a different type in each of the two possible ways, thus forming two different «isotope» types of a dizygotic twin.
  • the mosaic element 11 in FIG. 1 consists of the rhombuses 11a and 11b, which are composed in such a way that the "short" shape of the dizygotic twin is created, whereas the mosaic element 1 in FIG. 1 is composed of the same rhombus type so that the "Long” form of the dizygotic twin results.
  • the mosaic element 14 is the “short” shape of a dizygotical twin, the “long” shape of which represents the mosaic element 16.
  • FIG. 1 Although the construction of the mosaic elements shown in FIG. 1 was explained with the aid of FIGS. 1 and 2, it can be seen from the above explanations that the formation of the mosaic elements from the set of rhombuses is easily possible, without relying on the regular polygon that forms the basis of the parquet or mosaic pattern (tessellation) is to be referred to.
  • the rules for a polygon with 4q sides were explained.
  • the other possible polygons with an even page number are those with a page number p equal to 4 (q + '/ 2 ).
  • the set of rhombuses q contains pairs of different rhombus types and (2q + 1) specimens of each type. The total number of all rhombuses is therefore q (2q + 1).
  • the set of mosaic elements which, according to the invention, is formed from this set of rhombuses therefore consists of q (q + 1) mosaic elements.
  • each rhombus type is clearly defined by its acute angle and this angle is an integral multiple of 360 ° / p, the integer being no greater than q. The largest possible such angle is therefore less than 90 ° and therefore none of the rhombuses is a square.
  • the amount of rhombuses required to form the mosaic elements is easy to form and that the mosaic elements can be obtained from the set of rhombuses in a simple manner, even without reference to the regular square that the The basis for the mosaic pattern or surface-filling pattern is. To construct the mosaic element set, it is therefore not necessary to solve the mosaic puzzle.

Landscapes

  • Engineering & Computer Science (AREA)
  • Multimedia (AREA)
  • Finishing Walls (AREA)
  • Adornments (AREA)
  • Toys (AREA)
  • Diaphragms For Electromechanical Transducers (AREA)
  • Yarns And Mechanical Finishing Of Yarns Or Ropes (AREA)
EP80102350A 1979-04-30 1980-04-30 Mosaikelementsatz Expired EP0018636B1 (de)

Priority Applications (1)

Application Number Priority Date Filing Date Title
AT80102350T ATE3695T1 (de) 1979-04-30 1980-04-30 Mosaikelementsatz.

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
US06/034,245 US4223890A (en) 1979-04-30 1979-04-30 Set of tiles for covering a surface
US34245 1987-04-06

Publications (2)

Publication Number Publication Date
EP0018636A1 EP0018636A1 (de) 1980-11-12
EP0018636B1 true EP0018636B1 (de) 1983-06-08

Family

ID=21875196

Family Applications (1)

Application Number Title Priority Date Filing Date
EP80102350A Expired EP0018636B1 (de) 1979-04-30 1980-04-30 Mosaikelementsatz

Country Status (5)

Country Link
US (1) US4223890A (ja)
EP (1) EP0018636B1 (ja)
JP (1) JPS55151977A (ja)
AT (1) ATE3695T1 (ja)
DE (1) DE3063659D1 (ja)

Families Citing this family (16)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPS6083681U (ja) * 1983-11-16 1985-06-10 吉本　直貴 平行４辺形玩具
US4561097A (en) * 1984-10-09 1985-12-24 Florence Siegel Puzzle formed of geometric pieces having an even number of equilateral sides
US4620998A (en) * 1985-02-05 1986-11-04 Haresh Lalvani Crescent-shaped polygonal tiles
JPS61242255A (ja) * 1985-04-16 1986-10-28 加藤　俊彌 正六面体形モザイクタイルの施工方法
JPS6439787U (ja) * 1987-09-05 1989-03-09
US5314183A (en) * 1993-03-17 1994-05-24 Schoen Alan H Set of tiles for covering a surface
USD423691S (en) * 1997-02-18 2000-04-25 Peer van Neerven Construction element set
US6203879B1 (en) * 1997-10-24 2001-03-20 Mannington Carpets, Inc. Repeating series of carpet tiles, and method for cutting and laying thereof
US6309716B1 (en) * 1999-09-24 2001-10-30 Adrian Fisher Tessellation set
US6439571B1 (en) 1999-11-26 2002-08-27 Juan Wilson Puzzle
CN1220537C (zh) * 2000-05-04 2005-09-28 伯恩哈特·盖斯勒 结构元件组
US7721776B2 (en) * 2004-11-16 2010-05-25 Justin Louis K Tiles and apparatus, system and method for fabricating tiles and tile patterns
US9162139B2 (en) * 2010-02-01 2015-10-20 Mordechai Lando Cube puzzle
US9070300B1 (en) * 2010-12-10 2015-06-30 Yana Mohanty Set of variably assemblable polygonal tiles with stencil capability
US20160303472A1 (en) * 2014-01-28 2016-10-20 Rebecca Klemm Polygon puzzle and related methods
US11498357B2 (en) * 2019-06-20 2022-11-15 Certainteed Llc Randomized surface panel kit and surface panel system

Family Cites Families (15)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US1495576A (en) * 1922-04-07 1924-05-27 Crehore Albert Cushing Puzzle
DE1699722U (de) * 1955-02-28 1955-06-02 Plastik Werk Fiedler & Podey Ornament - mosaik - zusammensetzspiel.
DE1809445U (de) * 1960-01-05 1960-04-07 Richard Lehmann Mosaik-stein.
US3065970A (en) * 1960-07-06 1962-11-27 Besley Serena Sutton Three dimensional puzzle
DE1880258U (de) * 1963-06-25 1963-10-03 And Klein Fassfabrik Lammelle zur herstellung von mosaikparkett.
FR2039506A5 (en) * 1969-04-01 1971-01-15 Michalopoulos Spiridion Mosaic floors with joints of thermoplastic - material
DE1961945A1 (de) * 1969-12-10 1971-06-16 Brent Metal Works Ltd Tuerschliessermechanismus
US3665617A (en) * 1970-02-13 1972-05-30 Ina Gilbert Design elements for creating artistic compositions
US3637217A (en) * 1970-02-13 1972-01-25 Sherman Kent Puzzle with pieces in the form of subdivided rhombuses
JPS5317387B2 (ja) * 1973-01-17 1978-06-08
GB1385913A (en) * 1974-02-26 1975-03-05 Robinson A K Puzzle apparatus for recreational educational mind training or like purposes
US4063736A (en) * 1975-06-04 1977-12-20 Alexander Kennedy Robinson Puzzle apparatus
GB1548164A (en) * 1975-06-25 1979-07-04 Penrose R Set of tiles for covering a surface
JPS5317387U (ja) * 1976-07-22 1978-02-14
JPS54118282U (ja) * 1978-02-03 1979-08-18

Also Published As

Publication number Publication date
EP0018636A1 (de) 1980-11-12
DE3063659D1 (en) 1983-07-14
JPS55151977A (en) 1980-11-26
ATE3695T1 (de) 1983-06-15
US4223890A (en) 1980-09-23
JPH037395B2 (ja) 1991-02-01

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